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Determine whether f is differentiable at the given point. If f'(a) exists, give its value. HINT...
-/7.14 points WANEAC7 3.1.035. 0/6 Submissions Used The graph of fis given. Use the graph to compute the quantities asked for, if a - 6. HINT (See Examples 4-5.1 (If you need to use or -- enter INFINITY or -INFINITY, respectively. If an answer does not exist, enter DNE.) (a) lim f(x) (b) lim f(x) Need Help? Wh Talk is a Tutar | -/7.14 points WANEAC73.1.039. 0/6 Submissions Used The graph of f is given. Use the graph to compute...
(1 point) For each of the following, determine the exact value of c that allows the function to serve as the probability distribution of a random variable with the given range. If no such c exists, enter DNE for does not exist. a) f(x)-c r for a 1,2,...,4c1/10 b) f(x) = c-for x-1, 2, . . . c of(x)-c. - , . . . c for x- 1,2, 3 6
Let f be defined on an open interval I containing a point a (1) Prove that if f is differentiable on I and f"(a) exists, then lim h-+0 (a 2 h2 (2) Prove that if f is continuous at a and there exist constants α and β such that the limit L := lim h2 exists, then f(a)-α and f'(a)-β. Does f"(a) exist and equal to 2L? Let f be defined on an open interval I containing a point a...
16. (0/3 points) DETAILS PREVIOUS ANSWERS LARCALC10 1.3.507.XP. Consider the following function and its graph. -2 Use the graph to determine the limit visually (if it exists). (If an answer does not exist, enter DNE.) lim f(x) X-1 0 (6) lim Write a simpler function that agrees with the given function at all but one point.
a. Determine whether the Mean Value Theorem applies to the function f(x) = x + on the interval [3,5). b. If so, find or approximate the point(s) that are guaranteed to exist by the Mean Value Theorem. a. Choose the correct answer below. O A. No, because the function is continuous on the interval [3,5), but is not differentiable on the interval (3,5). OB. No, because the function is differentiable on the interval (3,5), but is not continuous on the...
2. Let f: R R be a continuous function. Suppose that f is differentiable on R\{0} and that there exists an L e R such that lim,of,(z) = L. Prove that f is differentiable at 1-0 with f,(0) = L. (Hint: Use the definition of derivative and then use mean value theorem) 2. Let f: R R be a continuous function. Suppose that f is differentiable on R\{0} and that there exists an L e R such that lim,of,(z) =...
(1 point) Determine whether the series converges, and if so find its sum. 1 (k+ 6)(k + 7) (Enter DNE if the sum does not exist.)
Compute f '(a) algebraically for the given value of a. HINT [See Example 1.] f(x) = x2 − 9; a = 1 Compute f '(a) algebraically for the given value of a. HINT [See Example 1.] f(x) = x3 + 9x; a = 5 Compute the derivative function f '(x) algebraically. HINT [See Examples 2 and 3.] f(x) = x2 − 8 Compute the derivative function f '(x) algebraically. HINT [See Examples 2 and 3.] f(x) = 2x − 1 Find the equation...
A function and its graph are given. Use the second derivative to determine each of the following. Check your results against the graph shown. f(x) = x3 - 6x2 + 5x + 6 f(x -6 -4 -2 LLLLL X 416 Determine the interval on which the function is concave up. (Enter your answer using interval notation.) Determine the interval on which the function is concave down. (Enter your answer using interval notation.) Locate the point of inflection. (If an answer...
part a and b a. Determine whether the Mean Value Theorem applies to the function f(x) x+ on the interval(-4,-3) b. If so, find or approximate the point(s) that are guaranteed to exist by the Mean Value Theorem a. Choose the correct answer below O A. No, because the function is not continuous on the interval (-4,-3), and is not differentiable on the interval (-4,-3). OB. No, because the function is differentiable on the interval (-4,-3), but is not continuous...