Suppose you're given that COS x < f ( x ) ≤ ex² According to the Squeeze Theorem, Olim f(x) x→0 = −1 lim f(x) = 0 x→0 lim f(x) 0

Q: Let f(x) = 1²-16 +4 1²-16 H-4 x > 0 I≤0 Find lim f(1)

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Q: tan 3x lim x→0 \ e2x – 1 3/2 O 1/2 O 2 O 2/3

A: Solution:GivenTo find the limit oflimx→0 tan 3xe2x-1=?Formula:ddxeax=aeaxddx tan ax=asec2 ax

Q: HOSPitars fule lim X->0+ ex-1 Hx

A: Given that limx→0+1x-1ex-1Solution :limx→0+1x-1ex-1limx→0+ex-1-xxex-1Applying L hospital…

Q: Q8. We shall formally show that if two functions f and q are both differentiable at c, then we have…

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Q: If lim f(x) = = co then f (x) XCOS cos² X00

A: Given- If limx→∞fx=∞ then fx=xcos1x To Prove- The above expression.

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

A: f(x)=x2+9

Q: Use the limit definition of the derivative to show that the derivative does not exist at x = a for…

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Q: tan(3x) lim x→0 2x2 + 4x

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Q: Let f and g be real functions. Show directly from the definitions that if f is everywhere continuous…

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Q: Use the graph of the given function f(x) below to find the following. If something does not have a…

A: Solution:

Q: The function f is continuous for all real numbers. If lim f(x) = 0, then what is lim xe-2x)? x-2 x-1

A: The function f is continuous for all real numbers  If limx→2f(x)=0then if we put x=2t then…

Q: Where is the function f(x) = if x 0 removable discontinuity? Is it a jump discontinuity?

A: A jump discontinuity occurs when right and left limit exists but are unequal .

Q: Зх + 1 1 lim x→0 sin x 5 2 3 1 2

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Q: I if X > 4 and J (X). 4X + 1 i1 X<4. Find lim f(x) x→4+

A: Given; f(x)=√x-1 if x&gt;4 and f(x)=x2-4x+1 if x&lt;4.

Q: Evaluate lim (1+x)/x x→0

A: Please see the answer in step 2

Q: 3. If f is a continuous function, what can you say about lim f(x)?

A: Given thatf is continuous To determinelimx→1f(x)

Q: limit of a function f(x) as x approaches c is always equal to f(x). True or false

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Q: x² if x >0 if x <0 3. Consider the function f(x) 3D Find lim f(x) if it exists or state it does not…

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Q: If 3x − 1 ≤ f(x) ≤ x2 − 3x + 8 for x ≥ 0, find lim x→3 f(x).

A: Here we use sandwich theorem Also known as squeeze theoremThis theorem states that , if gx≤fx≤hx in…

Q: Use the limit definition of the derivative to determine f '(2) if gnibnoqonos su snimals (T ni 4 =…

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Q: If lim x→0 f(x) + x + 1 x sin (3x) = -5, then lim x→0 f(x) + x + 1 x² is equal to

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Q: (sin(2x)+7x2-2х 3. lim x→0 х4+2х3+x2

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Q: 7. Explain why for any function g, limg(c +h) = lim g(x). Use this to show that f'(c) = lim f(x) –…

A: Consider the given function limh→0gc+h=limx→cgx

Q: Suppose f(-2)=0 g(-2) = 0 f'(-2) 5 g'(-2)=1 = and all functions are continuous. f(x) lim Z-2 g(x)

A: The given values are .To find the limit .