MATH 2100 C958 Calculus I

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Ace Your Test with MATH 2100 C958 Calculus I Actual Questions and Solutions - Full Set

Free MATH 2100 C958 Calculus I Questions

1.

Find the critical points of f(x) = x3− 3x + 2.

  • x = 1,−1

  • x = 0,3

  • x = ±√ 3

  • x = 1 only

Explanation

​​​​​​​


2.

A classroom example: If velocity v(t) = 2t + 3, what is acceleration at t = 1?

  • 0

  • 2

  • 3

  • 5

Explanation

Explanation

Acceleration is the derivative of velocity with respect to time. Differentiate v(t) = 2t + 3 to get a(t) = 2. Because this acceleration is constant, it does not depend on t. Thus, a(1) = 2. The value of v(t) or t does not affect the constant acceleration.

​​​​​​​Correct Answer

2


3.

Volume: rotate y = √x, x= 0 to 4, about y-axis (shells)?

  • 8π

  • 4π

  • 16π/3

  • 128π/5

Explanation

​​​​​​​


4.

Global max of f(x) = x ln⁡ x − x on (0,∞)?

  • At x = 1/e

  • At x = 1

  • At x = e

  • None

Explanation

​​​​​​​


5.

In class: ​​​​​​​?

  • xx(ln x + 1)

  • xxln ⁡x

  • xx−1

  • x ln ⁡x

Explanation

​​​​​​​


6.

Area under y = 4 − x2 from -2 to 2?

  • 32/3

  • 8

  • 16

  • 16/3

Explanation

​​​​​​​


7.

Work: stretch spring 0.2 m beyond natural, k = 500 N/m, work = ?

  • 10 J

  • 5 J

  • 20 J

  • 50 J

Explanation

​​​​​​​


8.

Evaluate ∫(2x + 3) dx

  • 2x + 3x² + C

  • 2x² + 3 + C

  • x² + 3x

  • x² + 3x + C

Explanation

Explanation:

The integral of a polynomial is found by applying the power rule for integration: ∫xⁿ dx = (xⁿ⁺¹)/(n+1) + C. For ∫(2x + 3) dx, integrate each term separately. The integral of 2x is x², and the integral of 3 is 3x. Combining these results gives x² + 3x + C as the general antiderivative.

​​​​​​​Correct Answer:

x² + 3x + C


9.

Normal line to y=ln⁡x at x = e?

  • y = -x + e + 1

  • y = x - e + 1

  • y = -e x + e² + 1

  • y = x + 1

Explanation

​​​​​​​


10.

Which of the following functions is continuous at (x = 0)?

  • ​​​​​​​

  • ​​​​​​​

  • ​​​​​​​

  • ​​​​​​​

Explanation

​​​​​​​


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