Evaluate the function at the given numbers( correct to six decimal places). Use the results to guess the value of the limit or explain why it does not exist. F(x)=e^x-1-x/x^2. X=positive and negative 1, 0.5, 0.1, 0.05, and 0.01. As the limit approaches 0.

Value of the limit is 0.5.

Step-by-step explanation:

Given,

When,

Correct upto six decimal places.

Now,

  form, applying L-Hospital rule that is differentiating numerator and denominator we get,

    form.

Limit exist and is 0.5. That is according to (1) we can see as the value of x lesser than 1 and tending to near 0, value of the function decreases respectively. And from (2) it shows ultimately it decreases and reach at 0.5, consider as limit point of F(x).  

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18