evaluate the first limit 13] 3. Differentiate the following. Simplify your answers. a. f(x) = (x-2)2 (x + 3)" 13...
3. (6 points each) Differentiate the following functions. Do not simplify your answer. a. f(x) = 2*+1 In (x+1) b. p(x) = [arctan (x)]3 c. Q(x) = ex-sec(x)
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- Part 1: Limit of a difference quotient Suppose f(x) = – 5. Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box). X - 2 (f(5 + h) – f(5) lim h0 Him ( 15 + ) - 109 ) = lim ( = lim h0 | Part 2: Interpreting the limit of a difference quotient - Part 1: The derivative at...
Prob.II. Differentiate the following functions, and simplify. 1. f(x) 2x-3 x+4 2. f(x) = x²(x - 2)* 3. f(x) = In (x V1 - x2) 4. f(x) = x2e-* 5. Find dy/dx = y' for the equation x2 + y2 = 25 and find y" (check H.W)
1. (+2) Let f(x) +23 and let ro 2 (a) Evaluate f at ro (b) Differentiate f(x). Evaluate at r o
#35,37
In Exercises 21 through 38, differentiate the given function and simplify your answer 21. f(x) (2x 3)14 22. fx) 23. f(x) = (2x + 1)4 24. f(x) = V 5x6-12 25. fx)-(a 4r3 78 26. ft) (3r 729)5 27, f(t) = V5 3x 28. f(x)=- (6x2 +5x+ 1)2 5rt_ V4x2 30. 4x +1 31. f(x)=: (1-x2)4 2 3(5x4 1)2 32. f(x) = (1-x2)4 (135) f(x) = (x + 2)3(2x-1)5 36. f(x) 2(3x 1)(5x 3)2 (1 -x 1 - 5x2...
Part 1 Limit of a difference quotient 4 Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box). Suppose (2) = - 2 (7+h)-(7) 1-10) lim A0 (0)-0 0 Part 2: Interpreting the limit of a difference quotient The limit of the difference quotient (your second answer) from Part 1 above is (select all that apply). A. the slope of the tangent line to the...
Please answer all, be explanatory but concise. Thanks.
Consider the function f(x) = e x a. Differentiate the Taylor series about 0 of f(x). b. ldentify the function represented by the differentiated series c. Give the interval of convergence of the power series for the derivative. Consider the differential equation y'(t) - 4y(t)- 8, y(0)4. a. Find a power series for the solution of the differential equation b. ldentify the function represented by the power series. Use a series to...
Evaluate the function at the given values of the independent variable and simplify. f(x) = 4x -- (a) f(2) (b) f(-2) (c) f( - x) (a) f(2)= * (Type an integer or a fraction. Simplify your answer.) (b) f(-2)= 3 (Type an integer or a fraction Simplify your answer) (c) f(-x) = 4x+, 1 (Simplify your answer)
If f(x) = x² – 2x and g(x)= 3 - x°, evaluate the following. a. (f+gX3) b. (g-f)(4) c. (fog)(1) d. a. (f+9)(3) = (Simplify your answer.) b. (g - f)(4)=(Simplify your answer.) c. (f.g)(1)-(Simplify your answer.) d. (-1) - (Type an integer or a simplified fraction.) Enter your answer in each of the answer boxes
5. Differentiate the following functions by filling in the chart. Original Function Rewrite Differentiate Simplify a. f(x)= V.x2 b. f(x)= c. f(x)= 4 3.x2 T d. f(x)= (5x)2