Calc 3. - Test review assignment questions (#30 & #31)

Differentiate y=(x²+x³)⁴

Differentiate y= x²-x+2 / √x

Differentiate y= x²sinπx

Differentiate y = t⁴-1 / t⁴+1

Differentiate y = ln(xlnx)

Differentiate y = √x cos√x

Differentiate y = √arctanx

Differentiate y = tan (t / t²+1)

Differentiate y = 3^xlnx

Differentiate y = (1-x^-1)^-1

Differentiate sin(xy) = x² - y

Differentiate y = log₅(1+2x)

Differentiate y = lnsinx - ½ sin²x

Differentiate y = xtan^-1(4x)

Differentiate y = cos (e√^tan3x)

Find f”(2) when f(t) = √(4t + 1)

find y” if x⁶ + y⁶ = 1

Evaluate lim as h→0 (t³/tan³(2t))

Find a parabola (y = ax²+bx+c ) that passes through (1,4) and whose tangent lines at x = -1 & x = 5 are 6 and -2 respectively

At what points on the curve y = sinx + cosx, 0 ≤ x ≤ 2π, is the tangent line horizontal?

Find the tangent & normal line, y = (2+x)e^-x at (0,2)

Find the tangent line and normal line of the curve x² + 4xy + y² = 13 at (2,1)

Evaluate lim h→0 ( ⁴√(16+h) - 2 / h )

Find the linearization for f(x) = √(25 - x²) near a = 3

Find the differential for y = xe^-4x then calculate at dx = 0.01 & x = 0

Find the differential for y = √(1 - t⁴) then calculate when dx = 0.2 & t = 3

Find the differential of y = (1-v²)/(1+v²)

Find the linearization for (1.999)⁴ then solve

A ladder 25ft long is leaning against a vertical wall, if the bottom of the ladder is pulled horizontally away from the wall at 3ft/sec, how fast is the top of the ladder sliding down the wall when the bottom is 15ft feet from the wall?

Two cars, one going east at a rate of 90 km/hr and the other going due south at the rate of 60 km/hr, are traveling toward an intersection of two roads. At what rate are the two cars approaching each other at the instant when the first car is 200m and the second car is 150m from the intersection?

A swimming pool is an inverted cone with height 20 meters and a radius of 5 meters. It is being filled with a hose that pumps water at a rate of 3 cubic meters per minute. When the water level is 2 meters, how fast is the water level rising? When the water is 10 meters how fast is the water level rising?