10. Consider the function f(r) = 3r + 1 over the interval [O.31. into 3 equal subintervals and evaluating f at the right endpoints (this gives an upper sum). (a) Use finite sum to approximate the arca under the curve over |0. 3] by dividing (0.3 (b) Find a formula for the Riemann Sum obtained by dividing the interval (0.3] into n equal subintervals and using the right endpoints for cach . Then take the limit of the sum of...
8. Use the Fundamental Theorem of Calculus to find F'(x) given F(x)= pos() In(t+1) 8. (5 points) Use the Fundamental Theorem of Calculus to find F"(x) given F(x) - KREME RE Juin(a) sec" (6)
Use part I of the Fundamental Theorem of Calculus to find the derivative of F(x)=∫4 x sin(t3)dt F′(x) =
Find the indicated integral. Check your answers by differentiation. 1) du The slope f '(x) at each point (x, y) on a curve y = f(x) is given along with a particular point (a, b) on the curve. Use this information to find S (x). 2) f'(x) = 9x2 - 8x + 2; (0,7) 2) A) f(x) - 3x3 - 4x2 + 2x - 7 B) Ax) = 3x - 8 C)/(x) - 9x3 - 8x2 + 2x + 7...
(11) Does the function f(x) = 3x2 + 5x – 2, defined for r € (-1, 1), satisfy the hypotheses of the Mean Value Theorem? Find x = c such that f'(c) is the slope of the secant line passing through (-1,f(-1)), and (1, f(1)).
Use the Fundamental Theorem of Calculus and the chain rule to find a derivative Question If F(x)=∫4x522ln(t2) dt, what is F′(x)? (Do not include "F′(x)=" in your answer.) Sorry, that's incorrect. Try again? Use the Fundamental Theorem of Calculus and the chain rule to find a derivative Question If F(x) = 1 2 dt, what is F' (2)? (Do not include "F'(x) ="in your answer.) In (t2) Sorry, that's incorrect. Try again? FEEDBACK VIEW ANSWER SUBMIT
6 that is continuous on the entire Note that F(x) = J-6 V44 +6 dt. So assume f(e) = V 24 + 6 real line. Use the Second Fundamental Theorem of Calculus, which states that, if f is continuous on an open interval I containing a, then for every x in the interval, d f(x). f(t) dt = dx Step 2 In this problem, F(x) = Live* +6 dt. Therefore, F'(x) = f(t) dt = f(x) = V Submit Skip...
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)...
(1 point) Book Problem 8 Use part 1 of the Fundamental Theorem of Calculus to find the derivative of F(x) = { "tan(e)dt F'(x) = 1
please do all 3 1. (3 points) Find the derivative of F(x) = (t +2) dt. (You may assume that æ is restricted to an appropriate interval (a, b), so don't bother with any issues about that.) 42.2 - - 6 d. 2. (4 points) Evaluate 2 - 3 3. (3 points) Solve the equation sint dt = 0 for x where < <