@ MyCCCC Single Sign-On X Bb Take Test: Final Exam - MAT X Bb MAT_271_Final_Exam_Spring X Mail - Walton, Alisha - Outlc X Q youth soccer near wake for X Blackboard Learn X + X https://coastalcarolina.blackboard.com/bbcswebdav/pid-4124413-dt-content-rid-23936342_1/courses/MAT-271-02W-122/MAT_271_Fi... to G K. to 11 of 14 Q + Page view A Read aloud T) Add text Draw Highlight Erase 18. (4 pts.) Find the derivative of y = 120227 by logarithmic differentiation. 19. (3 pts.) Find the derivative of f(r) = cot-1 (4x3 - 12x) . HINT: the formula sheet at the end of the exam would be particularly useful. 20. (3 pts.) Find 16 25612 + 49 dx. HINT: in the formula sheet, what does du repre- OneDrive . . . X sent? Compare this to our substitution method. Screenshot saved The screenshot was added to your OneDrive. 80F Rain OLDN W 8:23 PM 5/6/2022 2@ MyCCCC Single Sign-On X Bb Take Test: Final Exam - MAT X Bb MAT_271_Final_Exam_Spring X Mail - Walton, Alisha - Outlc X Q youth soccer near wake fort X Blackboard Learn X + X https://coastalcarolina.blackboard.com/bbcswebdav/pid-4124413-dt-content-rid-23936342_1/courses/MAT-271-02W-122/MAT_271_Fi... to G K. to 12 of 14 Q + Page view A Read aloud T Add text Draw Highlight Erase For problems 21-25, determine whether each assertion is true or false. If the assertion is true, quote or obtain a relevant result. If the assertion is false, give a counterexample or other justification. 21. (1 pt.) (T/F) (f(x) 9(2)) da - f f(x)dx - 9(x)dz. 22. (1 pt.) (T/F) Let f(x) = 3x - 2,x -1 The discontinuity at r = -1 is remov- able. 23. (1 pt.) (T/F) Let F(x) = (312 - ) dt. Then F'(x) = 3 4 3x-4044 - 1' 24. (1 pt.) (T/F) Suppose we wanted to evaluate dx -. After making the substitution x In x u = Inc, we have: d.x r Inc = udu. 80F OLD W 8:23 PM Rain 5/6/2022MyCCCC Single Sign-On X Bb Take Test: Final Exam - MAT X Bb MAT_271_Final_Exam_Spring X Mail - Walton, Alisha - Outlc X Q youth soccer near wake fort X Blackboard Learn X + X https://coastalcarolina.blackboard.com/bbcswebdav/pid-4124413-dt-content-rid-23936342_1/courses/MAT-271-02W-122/MAT_271_Fi... to G K. to 13 of 14 Q + [ Page view | A Read aloud T Add text | Draw v Highlight Erase BI. (BONUS: 5 pts.) Let f(x) = =. Find f(2022) (x) . BII. (BONUS: 5 pts.) Recall that f is an even function if f (-r) = f (x) for all x. Use the chain rule to show that if f is even and differentiable, then f' (-x) = -f'(1). That is, the derivative of an even function is an odd function. 80F 8:23 PM Rain OLONE w 5/6/2022MyCCCC Single Sign-On X Bb Take Test: Final Exam - MAT X Bb MAT_271_Final_Exam_Spring X * Course Hero X C Calculus question | Chegg.c x Content X + X https://coastalcarolina.blackboard.com/bbcswebdav/pid-4124413-dt-content-rid-23936342_1/courses/MAT-271-02W-122/MAT_271_Fi... To G K. to 14 of 14 Q + Page view | A Read aloud T Add text | Draw Highlight Erase USEFUL TRIGONOMETRIC LIMITS AND PROPERTIES sin x . lim 1-+0 - COST COST - 1 . lim lim = 0 T sin z tanz = - cos X . sin (a + 3) = sin a cos B + sin B cos o cos (a + B) = cos a cos B # sin a sin B FORMULAS FROM CHAPTER 5 Inverse Trigonometric Derivatives [sin-' (u)] = u' - [cos-1 (u)] = - u' V1 - u2 V1 - u2 d d -u' dx [tan ' (u)] = 1 + u2 do cot (u)] = 1 + u2 d u' da sec 1 (u)] = |uvu2 - 1 do (csc-1 (u)] = Juvuz - Trigonometric Integrals (beyond Sine and Cosine) tan xdx = In | sec x] + C cot xde = - In | csex| + C sec xdx = In | sec x + tan x| + C csexdx = - In | csex + cota| + C Inverse Trigonometric Integrals du Va2 - u2 = sin-1 (") + c du a2 + 212 - tan-1 ( u ) + C du 714/712 - 612 - see -1 ( ful ) + 80 F OLONE W 8:54 PM Rain 5/6/2022