Calculus I-III Practice Exams FREE Sample Exam

What is the average rate of change of f(x) = x^2 on [1, 3]?

4

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8

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2

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6

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How is f(x) = x^2 + 2x classified by symmetry?

Neither even nor odd

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Even, because the squared term is unchanged when x is replaced by its negative value

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Odd, because the linear term changes sign when x is replaced by its negative value

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Both even and odd, because it contains one term of each symmetry type together

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Why does the intermediate value theorem show that x^3 + x – 1 = 0 has a solution between 0 and 1?

The polynomial has degree three, and every cubic equation has three real solutions in total

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The polynomial is increasing, and increasing functions always cross every horizontal line

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The polynomial changes sign on [0, 1]

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The value at x = 1 is exactly zero, so the endpoint itself is the required solution point

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What is lim (x -> 0-) |x| / x?

-1

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1

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0

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The expression is undefined at every point

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What is the derivative of 4 sqrt(x)?

2 / sqrt(x)

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4 / sqrt(x), from keeping the original coefficient in front of the root unchanged

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2 sqrt(x), from multiplying the coefficient by the root instead of dividing by it

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1 / (2 sqrt(x)), from dropping the coefficient four before applying the root rule

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What is the derivative of e^x?

x e^(x – 1), by applying the power rule to the exponent

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e^(x – 1), by reducing the exponent by one in the answer

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0, because the base of the exponential is a constant number

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e^x

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What is the derivative of x^2 sin x?

2x cos x, from differentiating both factors and multiplying the results together

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2x sin x + x^2 cos x

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2x sin x – x^2 cos x, from subtracting the second term of the product rule formula

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x^2 cos x alone, because only the trigonometric factor is differentiated in a product

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What is the equation of the tangent line to y = x^3 at x = 2?

y = 12x – 8, obtained by subtracting the function value only once from the product

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y = 8x – 16, obtained by using the function value as the slope of the tangent line

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y = 12x + 16, obtained by reversing the sign of the intercept in the final equation

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y = 12x – 16

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What is the derivative of f(x) = cos(x^2)?

-sin(x^2)

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2x sin(x^2)

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-2x sin(x^2)

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-2x sin(x^2) cos(x^2)

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For x^2 + xy = 6, what is dy/dx at the point (2, 1)?

-5/2

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5/2

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-3/2

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-7/2

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A spherical balloon’s radius is increasing at (1/2) cm/s. How fast is its volume increasing when the radius is 3 cm?

6pi cm^3/s

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18pi cm^3/s

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36pi cm^3/s

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18pi cm^3/s plus 4pi cm^3/s

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What is the derivative of f(x) = sqrt(e^x + x)?

(e^x + 1)/sqrt(e^x + x)

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1/(2 sqrt(e^x + x))

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(e^x + 1)/(2 sqrt(e^x + x))

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(e^x + 1)/(2 sqrt(e^x + x)) + x

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Calculus I-III Practice Exams FREE Sample Exam — Fixed Set

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