Calculus Answers

A body oscillates with simple harmonic motion according to the equation x(t)=5sin(4pie.t+pie/4

(x in meters). At time t = 5 seconds what are : /(6 x

2.5mrks)

(a) the displacement (b) the velocity

(c) the acceleration (d) the phase of the motion

(e) the frequency (f) the period of the motion.

Suppose that the profit P obtained in selling x units of a certain item each week is

given by

p=50 √ 3 - 0.5-500(0<x<8000)

.

Find the rate of change of P with respect to x when x=1600.

g(x) = ax + b / x, x≠k

given g(2)-3 & g(-2)=5

a) value of k

b) the values of a and b

c) the value of h if g-1(h)=2 (is this inverse)?

with the given domain, find the ranges

a) f(x)=3-2x for -2<x<2 (the < have a _ below it)

b) f(x)=x^2 for -5<x<-2

what does the for means. ive been stuck with this two questions for hours any solutions would be appreciated TT

Let h(x) =f(x)/g(x) where h(x) is polynomial of x. f f(x) = x³-2x²-3x and g(x)=x-3,then find the number of real solutions of the equation h(x)=0 in the interval [-2.0, 2.0]

Suppose that the speed v (in ft/s) of a skydiver t seconds after leaping from a plane is given by the equation 𝑣 = 190(1 − 𝑒 − 0.168𝑡).

(a) Graph 𝑣 versus 𝑡.

(b) By evaluating an appropriate limit, show that the graph of 𝑣 versus 𝑡 has a horizontal asymptote 𝑣 = 𝑐 for an appropriate constant 𝑐.

(c) What is the physical significance of the constant 𝑐 in part (b)?

It is estimated that t years from now the tree plantation of a certain forest will be increasing at the rate of 3t ² + 5t + 6 hundred trees per year. Environmentalists have found that the level of Oxygen in the forest increases at the rate of approximately 4 units per 100 trees. By how much will the Oxygen level in the forest increase during the next 3 years?