(a) Use the Mean Value Theorem to show that, if smals x+1 x² +1' then there is a point c in (-1, 1) such that f'(c) = - oup SHIGU (b) Use L'Hôpital's Rule to prove that the limit f(x) = x³ + 3x² - 4 e-1-1 exists and to determine its value. lim I→1

Q: Evaluate the limit, using L’Hôpital’s Rule if necessary

A: We first try to find the limit by substituting x=1

Q: Let f be a function such that −x^2 < f(x) < x^2 for the interval [−10, 10]. Does the squeeze theorem…

A:

Q: Prove, using the formal limit definition of the derivative, that if f(x) = then f'(3) = - 1-2x x3 s…

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Q: Find the limit lim x→∞ (1+5/x)x lim x→0 ((e2x-1-x)/x2)

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Q: In (x) — х + 1 lim x² 2х + 1 x→1

A:

Q: 5) Evaluate the limit of the function f(x) -3x4+4x³+8 lim x→∞0 4x3-5x²+4x-3 -3x4+4x³+8 4x3-5x²+4x-3'…

A: To find the limit of given function

Q: I - 1 (а) lim 41 r + x² – 2x 21? + 3д + 1 (b) lim Iª – x²

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Q: aluate the limit lim x→1 ƒ(x)-ƒ(1) x-1 using the limit toolkit developed in class

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Q: The limit lim h→0 f(x) a = 1 = x^3 (1 + h)³ - 1 h represents f' (a) for some function f and some…

A: We know that: f'(x)=limh→∞f(x+h)-f(x)h and f'(a)=limh→∞f(a+h)-f(a)h.

Q: Find the limits as x →co and as x→ co. (If the limit is infinite, enter 'co' or '-co', as…

A: Step 1:Step 2: Step 3: Step 4:

Q: Let f(x) = (3x^2 + 16x − 12)/(x + 6). Find L such that lim x→−6  f(x) = L, and prove that the limit…

A: Let f(x) = (3x^2 + 16x − 12)/(x + 6). Find L such that lim x→−6 f(x) = L, and prove that the limit…

Q: If f and g are continuous functions with f(-1) = 3 and the following limit, find g(-1) _lim [2f (x)…

A: