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(1 point) Compute the derivative of F(x) if F(x) = 5 * 31 dt F'(x) = 0 08
E. Define f(x) = %* sink dt. (a) Prove that this integral is defined. (6) Compute f'(x) explicitly. (c) Prove that f' is continuous at 0.
6. If f(x) = 5,*v2 dt, then f'(3) is:
Let S f(w)dt = 6, f(x)dx = -4, log(x)dt = 12, 9(x) dx = 9 Use these values to evaluate the given definite integral: -3 (f(x) f(x) + g(x)) dx
6. Let f be a continuous function on R and define F(z) = | r-1 f(t)dt x E R. Show that F is differentiable on R and compute F'
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If f(x) = 2x arctant dt, then evaluate (A) 7/3 (B)1 (C) 2/4 (D) */2 (E) 2
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...
dx Determine x= f(t) for (t? +4t) 4x + 4,t> 0; f(1) = 3. dt For (1? + 4t) dx dt = 4x +4, x= f(t) =
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 < <
Let A(x)=∫(bounds 0 to x) f(t)dt, with f(x) as in figure.
Let A(z) = J f(t) dt, with f(z) as in figure. -1 -2 A()l has a local minimum on (O A(z) has a local maximum on (0, 6) at a 6.5
Let A(z) = J f(t) dt, with f(z) as in figure. -1 -2 A()l has a local minimum on (O A(z) has a local maximum on (0, 6) at a 6.5