What is the value of * cosx + sin2x + 1 lim x² – 7²

Q: compute lim as x goes to pi/2 from the right of (x-pi/2)tan(x)

A: Given f(x)=x-π2 tanx To find limx→π2+f(x)=limx→π2+x-π2 tanx

Q: Find the one-sided limit ( if it exsit)

A: The given limit is,

Q: Solve

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Q: Investigate lim sin

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Q: Verify the identity tanh2 x + sech2 x = 1

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Q: 2 4. lim x-3+ \3-x 4 9-x2,

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Q: Evaluate limx-->0 (sin 2x sin 9x)/(x^2) Without using L'Hospital's rule.

A: The given function is limx-->0 (sin 2x sin 9x)/(x^2)Use the expansion for sin x to simplify (sin…

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: Evaluate limx-->2 (sin(x-2))/(x^2+4x-12) Without L'Hospital's rule.

A: limx-->2 (sin(x-2))/(x^2+4x-12)Numerator = sin(x-2)Denominator = x2 + 4x - 12 = x2 +6x - 2x - 12…

Q: -1 lim tan(In x)

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Q: Evaluate the limit: lim 2x2 cos(3x) 2

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Q: Show that lim sin() does not exist.

A: if we put x= 0 than become sin (1/0) that is sin(infinite) so does not exist

Q: Which theorem shall be used to find the lim sin 60 0-0 20 Theorem 1:lim Sin X x-0 x 1 = 1

A:

Q: Compute sin ax lim z0 sin bæ

A: L’Hospital’s Rule : Suppose limx→af(x)g(x) = 00  or  limx→af(x)g(x) = ±∞±∞ where a can be any real…

Q: Find the upper bound on the error if tan (2x')~ 2x and x< 0.2 -1

A:

Q: Using the important lemmas from Sec 3.3, compute 2 tan(-6x) lim 3x

A: From the given problem:   limx→02tan-6x3x   So, limx→02tan-6x3x=-4limx→0tan6x-6x

Q: Find the Limit (sin3x)/(5x^3-4x)

A: Obtain the limit value as follows.

Q: F ind @ Dlim Ix16/ lim 1-cos 3x 9. 4-X lim (1-secx) lim CosO 9= (9 -) 2.

A: Note :- there is an error in part (a) in this part value of limit is wrong. So i am solving…

Q: Evaluate using substitution.

A: The given expression is limx→π4tan3x

Q: What is the value of cosx + sin2x + 1 lim x2 – 72

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Q: Evaluate the limit: lim 10x2 cos(4x) 10

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Q: 2ェ+ COS lim エ→ー 3.x - Vz?+3

A: I=limx→-∞2x+cosx3x-x2+3dividing x b N and…

Q: 7. Without using L'Hospital Rule, evaluate lim cos(xsinx) x3

A:

Q: Evaluate: 1- cos(x) 3x2 lim Express your answer in 4 decimal places.

A: According to question,Given limit,limx→0 1- cos x3x2

Q: Evaluate using Theorem as necessary.

A:

Q: cos(7x) – 3 + b lim- x-0 e2x – bx – 1

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Q: Prove that 2" + 2* -6 lim tan'x - 3tanx lim 2* -2 1-/3 cos (x+ p/ 6)

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Q: Use th Start! 1- cos 2x

A: Given:1-cos2x/cos2x To simplify we use some trigonometric properties

Q: lim = 0 sin x.

A: limx→01x-1sinx=0

Q: Prove that lim x-&gt;0+ √ x [1 + sin2 (2 π/x)] =0

A: Given: limx→0+x1+sin2 2πx By using the property of limit, the limit of a product is the product of a…

Q: -+inf In(tan¯1x) 1+x2 1

A: ∫1∞ln(arctan(x)1+x2dxSubstiute u=arctan(x)→dudx=11+x2→dx=(x2+1)du=∫ln(u)duIntegrate by parts…

Q: * Find the value of Tx³ + 2. lim [sin (- x3+1] -1 O

A:

Q: Show that lim |x|cos 0.

A: We have to prove that limx→0xcos1x4=0. Use property, if limx→a−fx=limx→a+fx=L then limx→afx=L. First…

Q: Find lim 1-CoS 3X Xう。 tan x -1 lim メー X - X->

A: Solution is given below..

Q: Prove that 2 +22- -6 lim 3, tan x-3tan x lim cos(x+7/6) V2* - 2-

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Q: Evaluate sin 5x) lim, 0 (sin 5z ) 3x O 1 O 3/5 O 5/3

A: Topic:- limit calculus

Q: Evaluate using substitution.

A: We have to calculate the following limit L:

Q: What is the lim (3)¯ I 7 sec (7x) cos(3x)?

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Q: 4 sin 7x lim x1 cos TX+x

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Q: Show that lim x|cos )= = 0.

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Q: lim (sec'x - tan'x) = ∞ tan’ x) = 0

A: To show indeterminate of limx→12π(sec3x-tan3x)=∞

Q: A func tion f is given. sin 4x f(x) = 2.x Is f even, odd, or neither?

A: We have to find type of function if fx=sin4x2x We know that  if we replace x with -x and after…

Q: Evaluate: lim-0 (cos 2x) 2²

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Q: Evaluate lim,→0 ela-cos 7x 8 sin x 7

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Q: lim 1-3 (r-3) tan(9-x²) sin²(2x - 6)

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Q: Evaluate using substitution. lim tan(3x) x→ π/4

A: Given: limx→π4 tan 3x To evaluate: The value of the limit.

Q: Evaluate limt--&gt;0 (sin 3t)/(sin 6t) WITHOUT using L'Hospital's rule.

A: The given function is limt--&gt;0(sin 3t)/(sin 6t).

Q: what is the domain restriction for tanx=cosx? I know that the domain is x= pie/2+piek

A: Given tan x =cos x As u know the domain of the function.

Q: Evaluate: lim       (1-cos-1x)csch(1-x) x→1-1

A: To evaluate: limx→1-11-cos-1xcsch(1-x)

Q: evaluate the limit.

A: Given limit is Since Therefore, by applying L'Hopitals' Rule, we have