Question 1 Evaluate the limit. Note: two 'o's make infinity (oo). sin(t) ‚ († — 1)²) lim t-0 11 -4et. 4t

Q: find the limit of the function given in * figure 1 tan 3x? + sin²5x lim x→0 x²

A: 1 .When limit is of the form 00  or  ∞∞  then L' Hospitals Rule is used. 2. In L' Hospitals Rule ,…

Q: a) Find the limits of the following functions: i. sin 2x lim o 2x +x V+ 12-4 lim X-2 x- 2

A: To find the limits of the following functions : (i)  limx → 0 sin 2x2x2 + x(ii)  limx → 2 x2 + 12…

Q: Find the limits in Exercis

A: Find the limit: limθ→0sinθsin2θ Solution: We know that, sin2θ=2sinθ cosθ Evaluating the limit.…

Q: lim ñ s Sin n 2n

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Q: Q.4: (A) Show that Lim t'i = 4 i t >2

A: The given symbol is the symbol of the limit of the function at the given point of limit.…

Q: 1 o. = 0. Show that lim x² sin -| *

A: Use the property that -1≤siny≤1. Take y=1x, then -1≤sin1x≤1

Q: What is the value of lim sin x χ→πχ-π ?

A: limit

Q: Show that

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Q: b. lim cos(x)-1 x2

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Q: 4 sin? r d) lim a-0 3x tanx

A: see below the answerHere we use the L'Hospital Rule islimx→af(x)g(x) is of the form 00 then…

Q: et sin x — х - lim x → 0 5 cos x – 5 ||

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Q: \(d\) is a metric on \(X\). Show that \(\rho : X^2 \to [0,\infty)\) defined by \[ \rho(x,y) =…

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Q: Find the limits

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Q: lim,-o ([sin x]*) is

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Q: Evaluate the limit.

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Q: Evaluate the limit (1 – cos x)² sin² . lim x2(1 – e)4 COS X - -

A: Given limit is : limx→01-cosx2sin2xx21-ex4  To find the value of the limit.

Q: (2) lim (cos x)¹/x² b Find the limits for values of x in radian system: (1) lim (cos x) ¹/x² x-0

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Q: 2 lim(cosx)x² =? x→0

A: Given: limx→0cosx2x2=limx→0cos2x2x

Q: lim (1 + 2 sin 3x) cotx = ? x →0

A: Here we have to evaluate the limit

Q: 61. lim r sinx 63 1:

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Q: Find the limits

A: Given limit:

Q: 2 + v - , 2+z+ 11. 0. di

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Q: QUESTION 10 Let fx)- 5x+x-2 and g(x)= x+13. Find the limit. %3D lim g(f (x)) O a. – /4 O b.17 O c. 4…

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Q: tan 3. lim 2t t→0 ´tan 3x' lim ( ) x→0 csc 3x 5. lim X-0 \3cotx,

A: Topic = Limits

Q: Find the value lim (cos z) z 2-0

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