Calculus Answers

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?

Use the implicit differentiation formula to find dy/dx for the equation arctan(x^2 y) = x + xy^2

Find the linearization of the function f(x,y) = ye^x + 2x^2 y at the point (0,2) and use the result to approximate f (0.1, 1.9) to three decimal places.

If y=sin2ax+cosax,prove that yn=a^n{1+(-1) sin2ax}^1/2