Question 1 5 pts If F(x) = x + 4 which of the following limits is...
#23. Use the limit definition of the derivative to show why f(x) = (x - 5) is NOT differentiable at x = 5. (Hint: Compare the left- and right-hand limits of lim nits of lim f(5+h)-f(5) 102.) Is f(x) = (x - 5)% continuous at x = 5? What does the tangent line at the point (5,0) look like? 0
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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...
4. Find the following limits. 473 + 5x² - 2x+2) 273 - 2x + 100 203 - +3 (b) limz+03,3 - 2x2 – 3x + 2 (a) limz+ f (x +h)-f(x) 5. Find the derivative using the definition /' () = lim-0- (a) f(x) = 22 - 2 (b) f(x) = 2x + 3 6. Find the derivative using the formula including product rule and quotient rule (Don't use the definition in # 5) 3.- 2 (a) f(x) = 33...
Question 17 5 pts Suppose f(x) = [Vť – 5t + 6.25 dt. For which positive value of x, does f'(x) equal O? 0 O 2.5 There is no such value of x. V2.5 O 1 Question 16 5 pts Use the Fundamental Theorem of Calculus to find the derivative, f'(x), of va t2 f(x) = S. dt. 4+ 3t4 1 x2 4 + 3x4 х 4 + 3x2 a 4 + 3x2 2 (4 + 3x2) -C 2+(4+ 3x2)...
Question 1
1. [5 pts] Give a complete definition of lim f(x) = -oo if... 2. [25 pts] Give an example of each of the following, or state one or more theorems which show that such an example is impossible: a. A countable collection of nonempty closed proper subsets of R whose union is open. b. A nonempty bounded subset of R with no cluster points. c. A convergent sequence with two convergent subsequences with distinct limits. d. A function...
Referring to the graphs given below, use properties of limits to find each limit. If a limit does not exist then state that it does not exist. y = f(x) y = g(x) lim f(x)= lim g(x) = f(x) x- lim x+0 g(x) lim lim g(x) = lim [f(x)+g(x)] = x-1 lim f(x) = lim g(x) = lim --+ f(x) h- h derivative of f(x) = 2x² + 3x is f'(x) = 4x +3. The steps are what count here!...
Question 1 (1 point) Use the figure shown to answer the following question aboutf(x). What is the limfm)? (-2,2), 2 (0.1) (3.0) I -4 -3 -2 - 1 2 4 5 (-2-1) (3-1) -1 -2 1) The limit does not exist. 2) The limit is 1 3) The limit is 3 4) The limit is 0. Question 2 (1 point) Question 2 (1 point) Use the figure shown to answer the following question. What is the lim f(x)? (6,5), (1.4)...
Using the definition of the derivative, find f'(x) for the following function. 3. f(x) = x2 + x - 1 the definition of the derivative f'(x) = lim f(x+h)-f(x) h h-0 What is the slope of tangent line to this curve at x = -1?
f(x) 12. If lim z = 5, find the following limits. (m) lim f(x) (b) lim
Calculus 1 MAT 201 Final Exam, Spring 1 2019, LAGCC Evaluate the following limits, you may use L'Hospital's rule, if it applies. -V31+4 lim 4-1 -4 a. b. Evaluate the following limit. lim xIn x x-0 2. Evaluate and explain your answer -xsin(x)+cos (x) x+1 130 dx (a.) 130 Differentiate each of the following below using the fundamental theorem of calc part 1 X cos? (1- 51) dt ) g (x) = S_ e (2c) g(t)= J x2t+1 3 Use...