Calculus

posted by .

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^x-1)/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 x-range, I cannot find y. I've tried the epsilon-delta scheme, but I'm having trouble understanding that. I'm in a pinch on this homework question.

  • Calculus -

    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

First Name
School Subject
Your Answer

Similar Questions

  1. 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 …
  2. 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 …
  3. 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 …
  4. 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, …
  5. 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, …
  6. Calculus

    (a) By graphing the function f(x) = (cos 2x − cos x)/x2 and zooming in toward the point where the graph crosses the y-axis, estimate the value of lim x → 0 f(x). (b) Check your answer in part (a) by evaluating f(x) for …
  7. Calculus

    (a) By graphing the function f(x) = (cos 2x − cos x)/x2 and zooming in toward the point where the graph crosses the y-axis, estimate the value of lim x → 0 f(x). (b) Check your answer in part (a) by evaluating f(x) for …
  8. 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 …
  9. 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 …
  10. 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 …

More Similar Questions