calc 1 (just checking)

If the position of a particle is represented by s(t) = t² + 2, what is its displacement at t = 1?

• Position = 0 ft
• Position = 1 ft
• Position = 2 ft
• Position = -1 ft

If the position of a particle is represented by s(t) = t² + 2, what is its average velocity from [0, 1]?  

• 1 ft/sec
• 2 ft/sec
• 3 ft/sec
• 4 ft/sec

If the position of a particle is represented by s(t) = t² + 2, what is its instantaneous velocity at t = 1?  

• 1 ft/sec
• 2 ft/sec
• 3 ft/sec
• 4 ft/sec

Find the derivative f(x) = (x² + 2x)⁵

• f'(x) = 5(2x+2)⁴
• f'(x) = 5(x² + 2x)⁴
•  f'(x) = 5(x² + 2x)⁴(2x)
• f'(x) = 5(x² + 2x)⁴(2x + 2)

Find the derivative of f(x) = x²sinx

• f'(x) = 2xsinx - x²cosx
• f'(x) = 2xsinx + x²sinx
• f'(x) = 2xsinx + x²cosx
• f'(x) = 2xcosx

Find the derivative f(x) = x²/e^x

• f'(x) = (x²e^x - 2xe^x) / (e^x)²
• f'(x) = (2xe^x + x²e^x) / (e^x)²
• f'(x) = (2xe^x - x²e^x) / (e^x)²
• f'(x) = x²e^x + 2xe^x

Differentiate f(x) =(2/ x⁵) - 5.

• x⁵-3
• -10x⁶ 
• x⁵-5
• -10x^-6 

• 1/2
• Does not exist
• 0
• 1/4

• 0
• -1
• infinity
• -infinity

lim_x→0 sin(6x) ∕ sin(2x)

• 1/3
• 3
• 1
• w