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Given that f(x) and g(x) are differentiable functions and the following function values are true, find h'(a) if h(X) = f(g(x)). f(a) = 4 g(a) = c g(c) = 10 f(c) = 15 f'(a) = 8 g'(a) = b g'(c) = 5 f'(c) = 6 A) 6b B) 8b C) -4b D) 15b

A

If y = sin x cos x, then at x = π/3, dy/dx = A) -1/2 B) -1/4 C) 1/4 D) 1/2

A

If f(X) = cos³ (4X), then f'(x) = A) 3cos³ (4x) B) -12cos²(4x)sin(4x) C) -3cos²(4x)sin(4x) D) 12cos²(4x)sin(4x)

B

If f(x) = x³ - x² + x - 1, then f(2) A) 10 B) 9 C) 7 D) 5

B

Let f be the function defined by f(x) = 2x + e^x. If g(x) = f⁻¹(x) for all x and the point (0,1) is on the graph of f, what is the value of g'(1)? A) 1 / (2 + e) B) 1/3 C) 1/2 D) 3

B

Let f be the function given by f(x) = (2x-1)⁵(x+1). Which of the following in an equation for the line tangent to the graph of f at the point where x = 1? A) y = 21x+2 B) y = 21x-19 C) y = 11x-9 D) 10x+2

B

WHat is the slope of the line tangent to the graph of y = ln(2x) at the point where x = 4? A) 1/8 B) 1/4 C) 1/2 D) 3/4

B

d x + 1 --- ( -------- ) dx x² + 1 A) x² +2X − 1 -------------- (X² + 1) B) -X² − 2X + 1 -------------------- X² + 1 C) -X² − 2X + 1 -------------------- (X² + 1)² D) 3X² + 2X + 1 ------------------ (X² + 1)²

C

For which of the following does lim f(x) = 0 x →∞ I. f(x) = ln x/ x⁹⁹ II. f(x) = e^x/ lnx III. f(x) = x⁹⁹/e^x A) I only B) II only C) III only D) I and III only

D

If f(x) = 4x⁻² + (1/4)X² + 4. then f(2) = A) -62 B) -58 C) -3 D) 0

D

If y = sin⁻¹ (5X), then dy/dx = A) 5 --------- 1 + 25x² B) -5 ------------ √(1-25x²) C) 1 ---------- √(1-25x²) D) 5 -------- √(1-25x²)

D

If y³ + y = x², then dy/dx = A) x/2 B) 2x/3y² C) 2x-3y² D) 2x/(1+3y²)

D

The line y = 5 is a horizontal asymptote to the graph of which of the following function? A) y = sin(5x)/x B) y = 1/ x-5 C) y = 5x/1-x D) y = 20x² - x / 1+4x²

D

lim 4x²-3x+2 / x → ∞ 5x -3x²+1 = A) ∞ B) -∞ C) 0 D) -4/3

D

lim x-3/ x →14+ x -14 A) 1 B) -∞ C) 0 D) ∞

D