This test: 21 point(s) E Test: SPRING 2022 UNIT TEST Question 7 of 21 possible 3 Ill (Application of Derivatives) This question: 1 Submit test "pint(s) possible Next question Evaluate the following limit, Use M'Hopital's Rule when it is convenient and applicable lim ( *% + x) , for some constant a X +0 . . . =(Type an exact anewer) X-+0Evaluate the following limit. Use I'Hopital's Rule when it is convenient and applicable. 13 In x - 13 lim x-e x- e Use I'Hopital's Rule to rewrite the given limit so that it is not an indeterminate form. 13 In x - 13 lim - = lim x-e x- e Evaluate the limit. 13 In x - 13 lim = (Type an exact answer.) x-e X- eThis test: 21 paint(s) E Test: SPRING 2022 UNIT TEST Ill (Application of Derivatives) Question 18 of 21 possible This question: 1 Submit test point(s) possible Suppose f(x) = Vx is to be approximated near x= - 8. Find the linear approximation to f at x= - 8. Then, complete the Linear Exact Percent following table, showing the errors in the various approximations. Use a calculator to obtain the exact values. The percent approx. value error error is calculated using the formula below. Comment on the behavior of the errors as x approaches - 9. -79 7.09 100 . | approximation - exact 7.989 exact 7.9999 6.0D0 1 - 8.001 - 8.01 - 8.1 Complete the linear approximation column of the table. ( Round to seven decimal places as needed.) Linear approx - 7.9 -7.99 -7.999Evaluate the following limit. Use I'Hopital's Rule when it is convenient and applicable. In (8x + 10) lim X-+00 In (3x + 2) +7 In (8x + 10) lim In (3x + 2) +7 (Type an exact answer.) X-+00This test: 21 paint(s) E Test: SPRING 2022 UNIT TEST