Calculus AB Problem Set 20-01 Five Good Problems—That may indicate you need to study more… 1. Given the integral

∫

12

0

1− x 2 dx and x = sin (θ ) , completely rewrite the integral in

terms of θ . [Note: This is not asking you for a value, it is asking you for an integral as your answer.]

2. [Calculator] Find y when x = 3 given that

dy = e x cos ( x 3 ) and y = 2 when x = 1 . dx

3. Find the domain of the function f ( x ) = ∫

t2 dt . 1− t

2x

2

4. [Calculator] Given that g ( x ) = f −1 ( x ) and f ( x ) = x 3 + 3x − 5 , find g′ ( 2 ) . 5. Find the value of k such that the line x = k passes through and divides the region bounded by f ( x ) = x 2 + 3x + 2 and g ( x ) = −x 2 − 5x + 1 into two equal parts. Threedecimal accuracy, obviously.

⎧ 2x + 1, x <1 ⎪ 6. Given the function f ( x ) = ⎨ ⎛πx π ⎞ ⎪ 4 − cos ⎜⎝ 2 − 2 ⎟⎠ , x ≥ 1 ⎩ a. Determine if the function is continuous at x = 1 . b. Determine if the function is differentiable at x = 1 . c. Find the average value of the function on the interval 0 ≤ x ≤ 3 .

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