If [ f(x)\dx<∞ show that limf(x)dx=0 k→∞00 1

Q: 3. Use a limit to find f'(4) for f(x) = x²-x.

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Q: (-3 if z 2

A: Here is a step by step solution of the problem. We have proved discontinuity at x=2 by evaluation…

Q: Let f(x) = x² + 9, x > 0. Find lim f'(x) →25

A: f(x)=x2+9

Q: Prob. 6 (a) i) Let f(x) = 2x² - 3. Find f'(-2) using only the limit definition of derivatives. (b)…

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Q: lim (x' – 2x* +5)= x→-2 O a. 22 O b. -11 O C. -13 O d. -18

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Q: Does limx → -1+ ƒ(x) = ƒ(-1)?

A: From the graph we see that at x=-1 there is a closed circle and the graph is right continuous at…

Q: Give an example of a function that is not continuous at x = 2 but limx→2 f(x) = 1

A: choose any equation of line such that f(2)=1 but the function function f(x) should be discontinued…

Q: X = (1-_-_-_-)* 2 o then f(x) tend:

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Q: If limit t y = f(x) write an expression for the differentia dy

A: Given: y=f(x)

Q: where is the function f(x)= llxll-2 continuous (or discontinuous)?

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Q: The equation of a tangent line at a point (x₁, f (x₁)) where limh→0 f(x₁+h)-f(x₁) h = +∞ is x = x1.…

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Q: Find the absolute extrema of f(x) infinity and "-oo" for negative infinity. - Since lim f(x)= x → ∞…

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Q: If f(x) = 5x² , then f' (x) = lim¬0 5(x+h)? –52? h True False

A: Given, If  fx = 5x2  ,  then  f'x = limh→05x+h2 - 5x2h We have to check the truthfullness of the…

Q: Let F(x) = | 3e“ dt. Find lim F(x) if it exists. If the limit does not exist, explain why. x→0

A: see below the answer

Q: show that the lim dose not exist x.y-00

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Q: f(a+ 3h)– f(a- 2h) When f' (a) =1 in the function f (x), obtain an extreme value of lim h h→0

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Q: Find the limit of the function along the path y = 2x X-1 lim (x.y)-(0,0) y -1

A: We have to find the limit of the function along the path