MATH 2100 C958 Calculus I

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Free MATH 2100 C958 Calculus I Questions

1.

d/dx [In |sec x|] = ?

  • tan x

  • sec x

  • cot x

  • 1

Explanation

​​​​​​​


2.

Apply the Mean Value Theorem to f(x) = x2 on [0,2]. What is the value of (c) in (0, 2) that satisfies the theorem?

  • √2

  • 2

  • 0

  • 1

Explanation

​​​​​​​


3.

Absolute min of f(x) = cos⁡ x on [0, 2π]?

  • -1

  • 0

  • 1

  • π

Explanation

Explanation:

The function cos⁡ x oscillates between -1 and 1. On the interval [0, 2π], the minimum value occurs when cos⁡ x = −1, which is at x = π. Therefore, the absolute minimum value of f(x) is -1.

​​​​​​​Correct Answer:

-1


4.

Quotient rule: d/dx(x2+1/x−1)?

  • ​​​​​​​

  • ​​​​​​​

  • ​​​​​​​

  • ​​​​​​​

Explanation

​​​​​​​


5.

Using the washer method: region between y = x and y = x3, rotate about y-axis, volume?

  • π

  • π/3

  • 2π/3

  • π/2

Explanation

​​​​​​​


6.

Area between y = sin⁡ x and y = cos ⁡x from 0 to π/4?​​​​​​​

  • √2​−1

  • 1

  • √2/2

  • 0

Explanation

​​​​​​​​​​​​​​


7.

Average value of f(x) = x2 on [0,3]?

  • 3

  • 9

  • 1

  • 4.5

Explanation

​​​​​​​


8.

Critical points: f(x) = x + sin⁡x

  • None

  • x = π/2 + 2kπ

  • x = −π/2 + 2kπ

  • x = kπ

Explanation

​​​​​​​


9.

Definite integral: ∫0πsin⁡x dx = ?

  • 1

  • 2

  • 0

  • -1

Explanation

​​​​​​​


10.

Rolle’s theorem: f(x) = x(x−1)(x−2) on [0,2], how many c?

  • 1

  • 2

  • 3

  • 0

Explanation

​​​​​​​


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