Worksheets of Calculus

Test your skills on Worksheets of Calculus by trying out Worksheets of Calculus worksheets. 39 Worksheets of Calculus worksheets available to gain expertise and excel in your grades. The worksheets on Worksheets of Calculus have been designed to offer a wide range of questions covering all details of the Worksheets of Calculus and are in compliance with the k-12 curriculum. Detailed answers will be provided after you have attempted the Worksheets of Calculus worksheet. Each worksheet will have around 10 questions and there are multiple worksheets available to try out. The last worksheet on Worksheets of Calculus was uploaded on 18 May, 2012

Length of Polar Curve worksheet
1. Find the length of a = θ 0 ≤ θ ≤ 1?
  - ½ (√2 + (ln (1 + √2))
  - ½ (√2 + (1 + √2)
  - ½ (ln (1 + √2)
  - √2 + (1 + √2)
2. What is the length of the segment a = 6 / (1 + cos r ), 0 ≤ r ≤ ?
  - 6.000
  - 6.428
  - 7.248
  - 7.000
Play Now
Continuity of function of two or more variable worksheet
1. Determine the continuity point where the function f(m,n) = 5m+3n, m≤-1, n≤1 is the continuous?
  - m = 1, n=2
  - m = 4, n = 4
  - m = 0, n=2
  - m = -2, n=-1
2. Determine the continuity point where the function f(m, n) = 6m-8n, m≤-1, n≤-4 is the continuous?
  - m = 0, n = -2
  - m = 4, n = 5
  - m = -3, n=-4
  - m = 1, n = 5
Play Now
Continuity of function of one variable worksheet
1. Calculate the continuity point where the function f(p) = 5p + 3, p ≤ 5 is the continuous?
  - p = 7
  - p= 4
  - p = 6
  - p = 8
2. Calculate the continuity point where the function f(p) = 4p-2, p≤4 is the continuous?
  - p = 5
  - p = 7
  - p = 9
  - p = 3
Play Now
Continuity of function in Calculus worksheet
1. Find the point where the function f (z) = 2z+3, z≤ -4 is the continuous?
  - z = -2
  - z = -4
  - z = 5
  - z = 3
2. Find the point where the function f(z) = 3z-8 , z≤3 is the continuous?
  - z = 3
  - z = 8
  - z = 5
  - z = 7
Play Now
Area Between Curves Worksheet
1. Calculate the area of region between two curves y = x² and y = ?
  - 1/4
  - 3/2
  - 1/3
  - 1/13
2. Calculate the area of region bounded by x = 2, y = x + 1 and y = and y- axis?
  - 4.521
  - 3.5092
  - 3.0000
  - 2.9090
Play Now
Constant Law of Limit Worksheet
1. Using constant law of limit solve the given problem, ?
  - 5
  - 7
  - 10
  - 25
2. Using the constant law solve the given problem ?
  - 2
  - 1.5
  - -7
  - 2.5
Play Now
Trigonometric Worksheet
1. Differentiate the function f (x) where f (x) = 3 sin (x) - 4 sin (x)?
  - 3 sin (x) + 4 cos (x)
  - 3 cos (x) + 4 sin (x)
  - 2 sin (x) + 4 cos (x)
  - 5 sin (x) + 8 cos (x)
2. Differentiate the function f ( x ) = x ³ tan ( x )?
  - x ²( x sec ² x + 3 tan x )
  - x² ( cosec ² x + 3 tan x )
  - x² ( sec x + 3 tan x )
  - x² ( sec x + 3 tan² x )
Play Now
Subtraction law of limit worksheet
1. Evaluate the limit lim_x→3[x+5], using the subtraction law?
  - -2
  - 2
  - 3
  - 4
2. Find the value of given function lim_x→0[1+4x], using the subtraction law?
  - 1
  - -1
  - 2
  - -2
Play Now
Area of Region Bounded by Parametrically Defined or Polar Curves Worksheet
1. Find the area of region bounded parametrically, when first polar curve f (ѳ) = sin ѳ and other polar curve is g(ѳ) = cos ѳ, and these curve s lie between [-π/2, π/2]?
  - 2
  - 0
  - 3
  - 1
2. Find the area of region bounded by parametrically where one polar curve is f (ѳ) = 2cos ѳ and other polar curve is g (ѳ) = sin²ѳ, and these curve s are lie between [-π/2, π/2] interval?
  - (π + 8)/2
  - (π - 8)/2
  - (π - 8)
  - 0
Play Now
Velocity and Distance Problems Involving Motion Along a Line Worksheet
1. A car starts moving straight with 50 miles/hr speed from Sydney and reach Melbourne in 120 minutes, then find out the distance traveled by car?
  - 100 miles
  - 120 miles
  - 125 miles
  - 123 miles
2. A train starts from station ‘A’ at 9.00 am and reaches station ‘B’ at 01.00 pm. If the speed of the train is 50miles/hr, then find the distance between ‘A’ and ‘B’?
  - 250 miles
  - 225 miles
  - 200 miles
  - 210 miles
Play Now
Fourier Series and Laplace Transform Worksheet
1. Find out the Laplace transform of the function given below:
  f(t) = t when 0 ≤ t ≤ ( ½ )
  f(t) = t – 1 when ( ½ )≤ t ≤ 1
  f(t) = 0 when t > 1?
  - (1/s²) [ (e^-s - 1) + se^(-s/2)]
  - (1/s²) [ (e^-s - 1) + se^(-s/2)]
  - (1/s²) [ (e^-s - 1) + se^(-s/2)]
  - (1/s²) [ (e^-s - 1) + se^(-s/2)]
2. Find out the Laplace transform of the function f(t) = (1/t²) (1 – cos t)?
  - s log s / √(s² + 1) + tan^-1 (3/s)
  - s log s / √(2s² + 1) + tan^-1 (2/s)
  - s log 2s / √(s² + 1) + tan^-1 (2/s)
  - s log s / √(s² + 1) + tan^-1 (1/s)
Play Now
Other Applications Involving the Use of Integral of Rates Worksheet
1. A bullet is fired vertically upwards from surface at 25 m / s. Find the height of bullet after 3.5 s?
  - 23.654 m
  - 32.765 m
  - 25.555 m
  - 27.475 m
2. If electric current represented as a function of time given by i = 0.5 – 0.4 t, in a calculator circuit. Find the total charge passing from a point in circuit in 0.60 s?
  - 0.45
  - 1.43
  - 0.54
  - 0.05
Play Now
Area of Region Worksheet
1. Find the area enclosed with the region of the following equations: u = k³ + k² -6k and the k-axis?
  - 352 / 5
  - 253 / 2
  - 765 / 3
  - 253 / 12
2. Find the bounded area enclosed with the given equations u = k² and u = 8 – k²?
  - 76 / 5
  - 64 / 3
  - 78 / 5
  - 64 / 5
Play Now
Power Rule Worksheet
1. Determine derivative of the function y = (-x²) using power rule?
  - -2 x
  - -3 x
  - - x
  - -4 x
2. Find d/dx (-1/x²) using power rule?
  - -1/x²
  - -3 x
  - 2/x³
  - -4 x
Play Now
Concavity and Points of Inflection Worksheet
1. Determine the concavity of f(x) = x³ –3x² −9x + 13 and identify any points of inflection of f(x)?
  - Concave downward on (−∞, 2) and concave upward on (2, + ∞), and function has a point of inflection at (0, 1)
  - Concave downward on (−∞, -1) and concave upward on (-1, + ∞), and function has a point of inflection at (0, 1)
  - Concave downward on (−∞, -1) and concave upward on (2, + ∞), and function has a point of inflection at (0, 1)
  - Concave downward on (−∞, 1) and concave upward on (1, + ∞), and function has a point of inflection at (0, 1)
2. Find the concavity of f(x) = x³ –6x² and identify any points of inflection of f(x)?
  - Concave downward on (−∞, 2) and concave upward on (2, + ∞), and function has a point of inflection at (2, 11)
  - Concave downward on (−∞, -1) and concave upward on (-1, + ∞), and function has a point of inflection at (2, 11)
  - Concave downward on (−∞, 2) and concave upward on (2, + ∞), and function has a point of inflection at (2, -16)
  - Concave downward on (−∞, 1) and concave upward on (1, + ∞), and function has a point of inflection at (0, 1)
Play Now
Volumes of Solid of Revolutions Worksheet
1. Find out the volume created by rotating the region bounded by the curves k = u², the u- axis and the line u = 2 about u axis?
  - 32 π / 5
  - 39 π / 7
  - 22 π / 5
  - 20 π / 7
2. If the region formed by the curves k = u², the k - axis and the line k = 9 is rotated about the k axis then find out the volume of the solid that is generated by the rotation of these curves?
  - (71 π) / 3
  - (71 π) / 2
  - (81 π) / 3
  - (81 π) / 2
Play Now
Fourier Cosine Transform Worksheet
1. Find the cosine transformation for Fourier series where function f(t) = cos (πpt)?
  - f(u) = ½ δ(u-p) + δ(u +)p
  - f(u) = ½ δ(u-p) + ½ δ(u -p)
  - f(u) = ½ δ(u-q) + δ(u q)
  - f(u) = ½ δ(u-p) + ½ δ(u +p)
2. Find the cosine transformation for Fourier series where function f(x) = e^ax where interval of this function is (-π, π)?
  - a_n = (a(-1)ⁿ sinh(aπ))/π(a²+n²)
  - a_n = (2a(1)ⁿ sinh(aπ))/π(a²+n²)
  - a_n = (2a(-1)ⁿ sinh(aπ))/π(a²+n²)
  - a_n = (2(-1)ⁿ sinh(aπ))/π(a²+n²)
Play Now
Areas of Bounded Region Worksheet
1. Find out the area bounded by two regions k = u² and k = √u?
  - 2/3
  - 3/2
  - 1/3
  - 3
2. Find out the area of the region enclosed by k = u e^(u2), k = u+1, u = 2 and the k-axis?
  - 2.489
  - 7.987
  - 4.905
  - 3.509
Play Now
Arc Length Worksheet
1. Determine the arc length of y = log (sec x) where ‘x’ lies between o to π/4?
  - log (√2)
  - log (√2 + 1)
  - log (√3 + 1)
  - log (√5 + 1)
2. Calculate the arc length of the function f(x) = x^3/2 over the interval [0, 1]?
  - 1.44
  - 2.45
  - 3.46
  - 4.44
Play Now
Applications of Integration Worksheet
1. Calculate the average value of the following function on the interval given, f ( x ) = x² - 5x + 6 cos ( πx ) on the interval [-1, 5/2 ]?
  - -1.620
  - 7.250
  - 2.620
2. Calculate the number ‘k’ that satisfies the mean value theorem for integrals for the function on the interval [ 1, 4 ], where f(t) = t² + 3t + 2?
  - 2.593
  - -5.593
  - 3.593
  - 4.593
Play Now
Velocity and acceleration vectors of Planar curves worksheet
1. Find the velocity vector of a particle whose equation of the motion is given as, x ( t ) = t ² + 5 t ³andy ( t ) = t ³ – t ⁵,
  here, ‘t’ is representing the time variable. Calculate the velocity vector at t = 3?
  - (141 , - 378 )
  - ( 200 , 475 )
  - ( - 378 , 141 )
  - ( 339, 219 )
2. Evaluate the acceleration vector for the particle whose equation of motion is given as, x ( t ) = t + 7 t ⁴, y ( t ) = 2 t + 3 t ², At time t = 2?
  - (997, - 5)
  - (112 , 6)
  - (244 , 5)
  - (336, 6)
Play Now
Comparison between Integration and Differentiation Worksheet
1. Suppose a function y = f (x) = x² – 6. Then Find the differentiation and integration of the function?
  - 2x; x³ / 5 – 6x + C
  - 2x; x³ / 3 – 6x + C
  - 2x; x² / 3 – 6x + C
  - 2x; x⁵ / 2 – 6x + C
2. Calculate the differentiation and integration of the function y = f (x) = 2x² – 3x + 5?
  - 4x – 3; 2 x³ / 3 – 5 x² / 2 + 7x + C
  - 4x – 3; 2 x³ / 3 – 5 x² / 2 + 5 x + C
  - 4x – 3; 2 x³ / 3 – 3 x² / 5 + 7 x + C
  - 4x – 3; 2 x³ / 3 – 3 x² / 2 + 5 x + C
Play Now
Addition law of Limit worksheet
1. Find the sum of limit using addition law where limit expression is Lim _x→2[x - 12]?
  - 3
  - -6
  - -10
  - 10
2. Find the sum of limit using addition law of limit, where limit is given as: Lim _x→3[2x²+ 18x]?
  - 72
  - -72
  - -70
  - 70
Play Now
Worksheet on Laws of Limit
1. Solve this limit by the addition law of limits, Lim _x→5(x + 2)?
  - 6
  - 7
  - 5
  - 8
2. Solve the given problem using quotient law, Lim _x→2x² -4 /x² +x -6?
  - 0
  - 2
  - 4/5
  - 3/2
Play Now
Product Rule Worksheet
1. Rewrite the following as single exponent using product rule, 4³ x 4 = ?
  - 256
  - -264
  - 265
  - 260
2. Evaluate y=(x²+2)(x+2), using product rule?
  - -x³+2x²+2x+4
  - x³+2x²+2x+4
  - x³+2x²+2x
  - x³+2x²+4
Play Now