Use L'Hospital's Rule to evaluate the following limits. ex-1 a) lim (x²-x³)e²x b) lim X118 x−0 tanx c) lim_(tan x) cos x X→(π/2)-

Q: Determine lim f(x) assuming that cosx < f(x) < 1.                   x→0

A: We first apply limit x approaches 0, on all sides of the given inequality.

Q: Find the following limits: (a) If lim x--> 3 ((?f(x)/2x) +1)?=2,find lim x→3 f(x) (b)  Find lim…

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Q: Use the limit definition of the derivative of the given function at the given value of x (if it…

A: Given functions are

Q: If lim f(x) = 2, and lim g(x) = 7 find: C→C I-C a) lim 4f(z) A C b) lim ln(g(x))

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Q: The slope of the tangent line to the graph of the function y = 2x3 at the point (2, 16) is lim2"…

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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: tan(3x) lim x→0 2x2 + 4x

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Q: L True False y -2 then x 1 lim f(x) = 0 y = f(x) 3 X

A: We have to find Lim x approaches to 1 f(x)

Q: Let sin(32) T f(x)=A, 5-√25- " x>0 x=0 x < 0. (a) Find _lim_ f(x) and lim f(x). (b) For what values…

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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: 5. Use L'H rule to find (a). lim Inz2 (b). lim (sin x)(In x).

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Q: Use L'Hopital's rule to evaluate lim(1 – 2 sinh(x)) sch(a).

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Q: If g is continuous at a and f (x)=(x² -a' )8(x). fir find f'(a). Hint: Use f'(x1) = lim S(x)-f(x,)…

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Q: lim 1-e*) X-0 x sin x

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Q: Use L'Hôpital's rule 4. lim x csc x x →0

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Q: lim f(x)=-5 f. f'(-3)=0 а. g. f'(-2) is undefined h. f(-1)=2 i. f'(-1)=0 j. f'(3)=0 b. f'(-5) is…

A: When there's no tangent line and thus no derivative at a sharp corner on a function

Q: Q \ Find the value of 8 > 0 that guarantee lim x-0 csc(1/x) = 0 in terms of ɛ?

A: Definition of limit: We know that, limx→af(x)=L               ...(i) For each ϵ&gt;0, there exists a…

Q: f (x) =  x^2 +2         x3         1. At what value is this function discontinuous, if any?…

A: Given function, f(x)=x2+2,     x&lt;310     ,      x=3-3+4x,   x&gt;3

Q: Find lim f (x) if, for all x, 9 cos (4x) <f (x) < 8x2 +9. lim f (x) = %3D

A: The given inequality is: 9 cos(4x)≤f(x)≤8x2+9

Q: Suppose lim f(x) = 60 and f'(x) is positive for all x. Assuming lim f'(x) exists, find its value. X→…

A: I have explained everything with in the solution. Please go through that.

Q: Let s(x)=sin(x)/x. Explain why it is true that Lim (X-> 2pi) s(x)=0

A: Let  sx=sinxx Explain why it is true that limx→2πsx=0

Q: solve using L'Hopital's Rule 7. Lim    1/(tan-1)2  -  1/x2    x->0

A: Given the limit as : limx→0 1tan-12-1x2 We need to find the limit by using L' Hopital's Rule. Let's…