sin (2x) cos (2x) csc (x) 2. Determine the limit of · xVx4 as x approaches 0

Q: 2x sin x is x-0 1-cos x lim A. 5 В. — 5 C. 4 D. - 4

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Q: 1-cos x lim sin x x→0

A: Given: limx→01-cosxsinx

Q: - i) By using L'Hopital Rule, find sinx lim x-0 e3x 1 ii) Given that a = sin V3 2, find, csca -1

A: In L Hopital's rule take the derivative of numerator and denominator separately and than put the…

Q: 5 Find a limit equal to In(2x – 1) dx.

A: We know that, ∫lnxdx=xlnx-x+C…

Q: lim (cos(9x)) (+) +0+x

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Q: Using the limit approach prove that: d/dx [ cos x ] = − sin x

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Q: cos x dx - In (1 +x) 1- cos x a) b) lim

A: Given: a)∫011-cos xx2dx b)limx→0ln1+x21-cos x

Q: (c) cos lim (tan x)°os x x-(플)-

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Q: -Vx+ 1+ In(x) e* lim + sin (x)cos(x)

A: Find the limit

Q: x sin 4x b. lim x-0 1-cos3x

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Q: =) lim cos 3x sec 7x Xー

A: 1) a) The given function is, limx→π2cos 3x sec 7x. limx→π2cos 3x sec 7x=00 Rewrite the given…

Q: Limit as x approaches 0 1-cos(x)/sin(x)

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Q: cos x 13. lim x→(T/2)* 1 – sin x

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Q: エ→2 x² -4 1- cos 2x 7) lim X sin x エ→0

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Q 3/ x-sin x A- Find lim,0 1-cos x.

A: Explanation and solutions is given below....

Q: 1- Cos(ux) lim x-)0

A: Given expression limx→01-cos4xx2 Recall the identity 1-cos2x=2sin2x limx→02sin22xx2

Q: 1+sin 2 x 1) Find the derivative of f(x) %3D 2 cos3 x

A: The given function is                                    y=f(x)=1+sin2x2cos3x…

Q: ∫(2 cos(x) − 7sinx(x))dx   Evaluate indefinite anti-differentiation

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Q: Express the limit as a derivative.

A: Given, limθ→πcos θ-sin θ+1θ-π

Q: f (x) = cos(x) f(x) = tan(sin(x)) g(x) = In(2x2 + 4x + 3)

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Q: tan2(3 + Ax) – tan? 3 (c) Compute lim by interpreting it as a derivative. Ar+0 Ar

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Q: Find minimum of sin(x + 3) – sin(x + 1) – 2 cos(x + 2) where a E R.

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Q: xn²+1. lim, cos( x0 cos(*+1) x² +3 limx→0+ *国

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Q: sinx Q1//A- f(x) = cosx x < Required: lim f (x) 4

A: To check the limit of the function at pi/4 , we check it's left hand limit and right hand limit at…

Q: limit x to infinity (1+sin(3/x))^x

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Q: 2y-n у-п lim п cos y y-

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Q: x cos (3x – 7) cos(2x+ 7) lim cos(플-x)

A: Limits

Q: 71. Prove the reduction formula tank x dx = tan" k-1 х | tank-2 x dx k – 1 Hint: tank x = (sec² x –…

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Q: 12. Find the first derivative of y = 2cos(2 + x*). A. -4x sin (2 + x2) B. 4x cos (2 + x*) C. x sin…

A: Questiopn no. 12,Given,           y=2cos2+x2To find : The first derivative of the function.

Q: cos x In (1 + x) a) dx. b) lim 1 - cos x

A: Given: ∫011-cos xx2dx limx→0ln1+x21-cos x

Q: 4x 3-limx-0 tan5x sin(cos y) 4-lim, y- 2

A:

Q: 5. Use the concept of limits to find derivative of f(z) = (2z + 1)3 at z = -i.

A: Given function is f(z)=2z+13 We have to find the derivative of the given function at z=-i.

Q: Find the limit of the trigonometric function.

A: The given expression is limx→0cosx-sinx-12x

Q: 2 sin (4x) lim 2. x2 (1+ cos x)

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: find the limit as x approaches 0. 12sin(3x)/1-cos(3x) = as x approaches 0

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Q: f (x) = 4 sin(3x + 7) is continuous at every point x = x0; that is, lim 4 sin(3x + 1) = 4 sin(3xo +…

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Q: e*+ cos x (d) h(x) = tan x (e) y = Vx sec x e* =dx.secX.さャx.d secxrが4リxのsecX.àビ…

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Q: 1-2 c) dx

A: Evaluate the integral: ∫01e1-xdx. Simplify- ∫01e·e-xdx Apply ∫afx dx = a∫fx dx here a is constant.…

Q: lim as x approaches 0   x sin(x)/1-cos(x)

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Q: 1.) lim 2x sin'x. *P0 ex - x - 1

A: We apply l- hospital rules and solve it. Follow 2nd step.

Q: x+xcosx lim x-0 sinx cosx

A: We have to find the limit of (x+xcosx)/(sinxcosx) as x tends to 0

Q: sec2x-2taпх lim X→T/4 1+cos4x

A: Consider the given limit limx→π4sec2x-2tan x1+cos4x   limx→π4sec2x-2tan x1+cos4x=00 Which is…

Q: Find a limit equal to (x2 – 8)dx. 3

A: The integral of some functions are given below. 1)∫x2dx=x33+c2)∫8dx=8x+c Use the above and find the…

Q: 1 lim, (e** - 1)sin-+9cos x . x0

A: Given: limx→0ex2-1sin1x+9cosx we know that  limx→0ex2-1=0 and  limx→0sin1x=-1 to 1 so,…

Q: Express the limit as a definite integral on the given interval. lim [9(x;)³ – 9x;14x, [2, 8] i = 1…

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Q: Find the limit of sin2x/sin3x as x approaches to 0.   a. 1 b. 1/2 c. 0 d. 2/3

A: here we must know about  L'Hopital's rule to solve the given problem which is used whenever we…

Q: f(x) = /tan-1 (cos x) + In(sec x)

A:

Q: ez - x - 1 lim 1-0 -1+cos r COS T

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Q: 3 Find the maximum and minimum values for f(x) = - 4-(/2 cos x - V2 sin x)

A: Topic = Functions Maximum value of f(x)=1.5 Minimum value of f(x)=0.5

Q: Find the limit. 2. (2 sin x+2 cos´y+4 sec lim P→(2,2,0)

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Q: x*cos (x²) 1 – cos 3x lim X-0

A: we have to find the limit of the given expression

Q: 1. lim 3r+2r+1 X-n Sx2+7x+4 2. lim +sinx

A: See 2nd step