Evaluate the function f(x) at the given numbers. (Round your answers to six decimal places.)f(x) = 5ex − 5 − 5xx2, x = 1, 0.5, 0.1, 0.05, 0.01, −1, −0.5, −0.1, −0.05, −0.01f(1) = f(0.5) = f(0.1) = f(0.05) = f(0.01) = f(−1) = f(−0.5) = f(−0.1) = f(−0.05) = f(−0.01) = Guess the value of the limit of f(x) as x approaches 0. (Round your answer to six decimal places. If an answer does not exist, enter DNE.)lim x→0 5ex − 5 − 5xx2 =

To evaluate the function f(x) at the given numbers, we substitute each number into the function and calculate the result.

The function is f(x) = 5e^x - 5 - 5x/x^2.

1. f(1) = 5e^1 - 5 - 5(1)/(1)^2 = 5e - 5 - 5 = 5(2.71828) - 5 - 5 = 8.59140
2. f(0.5) = 5e^0.5 - 5 - 5(0.5)/(0.5)^2 = 5(1.64872) - 5 - 5 = 3.24360
3. f(0.1) = 5e^0.1 - 5 - 5(0.1)/(0.1)^2 = 5(1.10517) - 5 - 5 = 0.52585
4. f(0.05) = 5e^0.05 - 5 - 5(0.05)/(0.05)^2 = 5(1.05127) - 5 - 5 = 0.25635
5. f(0.01) = 5e^0.01 - 5 - 5(0.01)/(0.01)^2 = 5(1.01005) - 5 - 5 = 0.05025
6. f(-1) = 5e^-1 - 5 - 5(-1)/(-1)^2 = 5(0.36788) - 5 - 5 = -6.83960
7. f(-0.5) = 5e^-0.5 - 5 - 5(-0.5)/(-0.5)^2 = 5(0.60653) - 5 - 5 = -6.96735
8. f(-0.1) = 5e^-0.1 - 5 - 5(-0.1)/(-0.1)^2 = 5(0.90484) - 5 - 5 = -6.47580
9. f(-0.05) = 5e^-0.05 - 5 - 5(-0.05)/(-0.05)^2 = 5(0.95123) - 5 - 5 = -6.24385
10. f(-0.01) = 5e^-0.01 - 5 - 5(-0.01)/(-0.01)^2 = 5(0.99005) - 5 - 5 = -6.04975

To find the limit of f(x) as x approaches 0, we substitute 0 into the function:

lim x→0 5e^x - 5 - 5x/x^2 = 5e^0 - 5 - 5(0)/(0)^2 = 5 - 5 = 0.

So, the limit of f(x) as x approaches 0 is 0.