Test 2 Review PDF

𝑑𝑦 1) Find 𝑑𝑥 for each function. Do not simplify your answers. a) y = (7x5 − 6x)17 b) y = 4√tan 𝑥 c) y = ecsc x 2 +1 d) y=2𝑥 e) y=arccos( ln x) f) y=xcos x g) y=log 2 (3𝑥 + 1) h) y=𝑥 3 ln 𝑦 + log10 𝑥 − 1 𝑥 i) y=arccot 𝑥 𝑑2 𝑦 2) Find 𝑑𝑥 2 given y=arcsin x. ...

𝑑𝑦 1) Find 𝑑𝑥 for each function. Do not simplify your answers. a) y = (7x5 − 6x)17 b) y = 4√tan 𝑥 c) y = ecsc x 2 +1 d) y=2𝑥 e) y=arccos( ln x) f) y=xcos x g) y=log 2 (3𝑥 + 1) h) y=𝑥 3 ln 𝑦 + log10 𝑥 − 1 𝑥 i) y=arccot 𝑥 𝑑2 𝑦 2) Find 𝑑𝑥 2 given y=arcsin x.  𝑑2 𝑦 3) Given y = x cos y. Find 𝑑𝑥 2 terms of x and y. 4) Find an equation of the line tangent to the graph of the curve x3 + y3 = 9xy at the point (2,4) 5) The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is decreasing at a rate of 2 cm2/min. At what rate is the base of the triangle changing when the altitude is 10 cm and the area is 100 cm2? 6) Gas escapes from a spherical balloon at the rate of 20 cubic feet per minute. How fast is the radius changing at the instant the radius is 2 feet? 7) An airplane is flying at an altitude of 6 miles and passes directly over a radar antenna. When the distance between the plane and the antenna is 10 miles, it is increasing at a rate of 400 miles per hour. What is the speed of the plane? 𝑥 8) Find the differential of the function y =sin 𝑥. 9) Find the absolute maximum and minimum of the function f(x)=2x3 – 9x2 – 3 on the interval [–1,1] 10) A particle moves according to a low of motion s(t) = t3 – 13t2+ 35t – 15, t≥0, where t is measured in seconds and s in feet. a) Find the velocity at time t. b) What is the velocity after 3 seconds. c) When is the particle at rest? d) When is the particle moving in the positive direction? e) Find the total distance traveled in the 1st 8 seconds. f) Find the acceleration at time t.