Question

Evaluate h(x) for the following values of x?
Consider the following function.
h(x) = (tan(x)-x)/x^3

(a) Evaluate h(x) for the following values of x. (Give your answer correct to six decimal places.)


x =
a) 1
b) 0.5
c) 0.1
d) 0.05
e) 0.01
f) 0.005

what is f(x)

(b) Guess the value of the limit of h(x) as x approaches 0. (If it does not exist, enter NONE.)

Answer 1

We want to "guess" that limh(x)=1/3 if x->0
h(1)=(tan(1)-1)/1^3=0.557408
h(0.1)=0.334672
h(0.005)=(tan(0.005)-0.005)/0.005^3=0.333342