Calculus
posted by Sofia .
Consider the function f(x)=(5^x−1)/x.
A) Fill in the table values for f(x):
x= 0.1, 0.01, 0.001, 0.0001, 0.0001, 0.001, 0.01, 0.1
f(x)= 1.4866, 1.5866, 1.6081, 1.6093, 1.6096, 1.6107, 1.6225, 1.7462
B) Based on the table values, what would you expect the limit of f(x) as x approaches 0 to be?
lim (5^x1)/x= 1.60
x>0
C) Graph the function to see if it is consistent with your answers to parts (a) and (b). By graphing, find an interval for x near zero such that the difference between your conjectured limit and the value of the function is less than 0.01. In other words, find a window of height 0.02 such that the graph exits the sides of the window and not the top or bottom. What is the window?
_____ <_ x <_ ________
______ <_ y <_ _________
So far, everything I've done is correct for a and b. The online program we use for turning in homework allows us to preview the correctness of our answers. My issue is finding part C. When I use 0.02 and 0.02 for the xrange, I cannot find y. I've tried the epsilondelta scheme, but I'm having trouble understanding that. I'm in a pinch on this homework question.

I assume you used a calculator to find f(x) for the given values of x
Why are you having difficulty finding f(.02) and f(.02) ?
my calculator gives me
f(.02) = 1.5836..
f(.2) = 1.6356..
so
.02 ≤ x ≤ .02
1.5836 ≤ y ≤ 1.6356
Respond to this Question
Similar Questions

Calculus
For each value of h, evaluate the following function. Round your answer to four decimal places. lim h>0 (4+3)^(3)64/h A) h=0.01 B) h=0.001 C) h=0.0001 D) h=0.01 E) h=0.001 F) h=0.0001 For A I got 48.9 For B I got 48.99 For … 
Calculus
For each value of h, evaluate the following function. Round your answer to four decimal places. lim h>0 (4+h)^(3)64/h A) h=0.01 B) h=0.001 C) h=0.0001 D) h=0.01 E) h=0.001 F) h=0.0001 For A I got 48.9 For B I got 48.99 For … 
Calculus
Consider the function f(x)=sin(5x)/x. (a) Fill in the following table of values for f(x): x= 0.1 0.01 0.001 0.0001 0.0001 0.001 0.01 0.1 f(x)= ( I need the values of f(x) for each x) (b) Based on your table of values, what would … 
Calculus
Consider the function f(x)=(4^x−1)/x. (a) Fill in the following table of values for f(x): x= 0.1 0.01 0.001 0.0001 0.0001 0.001 0.01 0.1 f(x)= I the the falues of f(x) for each interval... (b) Based on your table of values, … 
Calculus
Consider the function f(x)=(4^x−1)/x. (a) Fill in the following table of values for f(x): x= 0.1 0.01 0.001 0.0001 0.0001 0.001 0.01 0.1 f(x)= I the the falues of f(x) for each interval... (b) Based on your table of values, … 
Calculus
(a) By graphing the function f(x) = (cos 2x − cos x)/x2 and zooming in toward the point where the graph crosses the yaxis, estimate the value of lim x → 0 f(x). (b) Check your answer in part (a) by evaluating f(x) for … 
Calculus
(a) By graphing the function f(x) = (cos 2x − cos x)/x2 and zooming in toward the point where the graph crosses the yaxis, estimate the value of lim x → 0 f(x). (b) Check your answer in part (a) by evaluating f(x) for … 
Math
Given table, X (1+x)^(1/x) 0.5. 4 0.1 2.8680 0.01 2.7320 0.001 2.7196 0.001 2.7169 0.01 2.7048 0.1 2.5937 0 5 2.25 From the table, show that lim x>infinity (1+x)^(1/x)=e. Plz someone show me the step how to show it based on … 
Math
Given table, X ; (1+x)^(1/x) 0.5. ; 4 0.1 ; 2.8680 0.01 ; 2.7320 0.001; 2.7196 0.001 ; 2.7169 0.01 ; 2.7048 0.1 ; 2.5937 0 5 ; 2.25 From the table, show that lim x>infinity (1+x)^(1/x)=e. Plz someone show me the step how to … 
math please help me!
Estimate the instantaneous rate of change of the function f(x) = x ln x at x = 1 and at x = 3. (Use h = 0.1, 0.01, 0.001, 0.0001, and so on. Round your answers to four decimal places.) f '(1) = f '(3) = What do these values …