cOs x tan x 28) lim x→0 sin 3x 29) lim x→0 2x x3 + 2x2 + x 30) lim x→-1 x4 + x3 + 2x + 2

Q: cOs x tan x 28) lim sin 3x 29) lim x→0 2x x3 + 2x2 + x 30) lim x→-1 x4 + x3 + 2x + 2 x3 – 2x2 + 4x –…

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Q: Find sin(x/2), cos (x/2) and tan(x/2) from the given information  sin(x) = 8/17 , 0° < x < 90°…

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Q: 2 cos(4x) – 4x? – 2 - - 8. lim x→0 sin(2x) – x2 – 2x -

A: Topic = Limits

Q: write sin(3x)cos(6x) + cos(3x)sin(6x) as a single trig function

A: This question is related to Trigonometric identities, we will solve it using given information.

Q: tan x sec X 3 10 cos xdydx

A: Given : Double integral ∫0π/2∫0tan x sec x y3 cos10x dydx   To find : Evaluate the given double…

Q: 6. cos x(csc x secx) secx) cotx

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Q: Compute Lim メーフ4 7x+5 -3 Sin ? X 2)x-70 3X イメ2+2 3) -00 X-7-00 2x-1

A: (1)Consider the given function with limit:

Q: 2 cos(8x) – 8 x² – 2 lim - sin(3x) — 2? — За

A: Here we apply l Hopital's rule.

Q: find integral tan 5 x sec 7 x dx

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Q: Find the limit

A: We have to find out the limit of given function Farmula used- (a-b) (a+b) = a^2-b^2 1-cos2x=sin2x

Q: prove tany csc3-tanX =cos x CSCX Sinx tanx tcosX-

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Q: 10) lim TT X-- sinx-cosx - TT X- 4

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Q: Suppose: sin(x) = -0.6638 cos(x) = 0.7479 tan(x) = -0.8875 Then, sin(-x) = 0.6638 cos(-x) 0.7479…

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Q: 4 tan(x) sec2 (x) tan(x) + 1

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Q: 2 cos(5x) – 5 x² – 2 sin(3x) – x2 – 3x - lim - - (Write your answer in the given box)

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Q: tan (5x) x sin3 (2x) 2)- limx-o:

A: we have to evaluate the A=limx→0tan4(5x)xsin3(2x)

Q: Suppose that x = 2 tan 8. What is sec e equal to in terms of x? √4+x² 2 √4+x² X Option 1 Option 2…

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Q: Exercises To Solve [No.5] Lim 5 9-5 dx -x²8x-15 D "Cosx dx Sin x+25inx+5 b

A: 5)  Let , I = lima→5 ∫a-4 dx-x2 - 8x - 15 Let , us simplify denominator first ,  -x2 - 8x - 15 = -x2…

Q: (tan'x de 3 1. [cse* xdx 4 2. csc"xdx 3. |tan 3x sec 3xdx

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Q: 1 1 Prove -2 secx tan x 1+ sin x 1- sin x

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Q: Lim as x approaches 0  1-cos(5x)+sin(3x)/x

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Q: tan(1 – x) 2 limx→1 2x +x – 3

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Q: 2. * 1 Add File 3. * 1 y = tan x + =tan³x 3 4. * y = = cos x 1 Add File y 1 cos³x 3 1 cosx

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

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Q: Find sin(x/2) =  cos (x/2) = tan(x/2) =   from the given information. sin(x) = 24/25,   0° < x <…

A: Question: Find sin(x/2) =  cos (x/2) = tan(x/2) =   from the given information. sin(x) = 24/25,…

Q: Show that limx→0(√x) cos(1/2x) = 0.Show your work.

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Q: 1 If f(x) = 8 tan¯¹(8 sin(2x)), f'(x) =

A: Differentiate

Q: 7- I = [sec(2x) tan(2.x)dx cos(2x) 8- I = dx 4-sin (2x) csc (In(x)) 9. I: dx

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Q: 1-cos 5x cOS lim 6x

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Q: In(|tan(x) sin(x)|) = 2 In(|sin(x)]) + In(|sec(x)])

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Q: 1-cos2.x sin 2.x : tanx

A: Given- 1-cos2xsin2x : tanx To Simplify- The above expression. Formula Used- cos2x=1-2sin2x and…

Q: Establish the identity.

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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: If cos(x)=sin(x)=0.5 , find the following:   1) (sec(x))^3 2) sin(2x)+(cos(x))^2 3)…

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Q: 1 (tan x + cot х) sec x %D 1/cosx 1/sinx 1

A: Given query is to find the correct option for the expression.

Q: lim, 0 6 tan² (5x) 15x²

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Q: If f(x) = sinx + cosx sinx - cosx 2 show that f'(x) = sin 2x – 1

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Q: from the given information. tan(x) = 2,   0° < x < 90° sin x/2= cos x/2= tan x/2=

A: Given tan(x) = 2 So first find x ,   where 0° &lt; x &lt; 90°

Q: [((1-tan^2(x))/sec^2(x)]= cos(2x)

A: To prove that  [((1-tan^2(x))/sec^2(x)]= cos(2x)

Q: lim sin (xt3) dt X 5

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Q: 9. Prove: csc(x)-csc(x)cos² (x) = sin(x)

A: To prove: csc(x)-csc(x)cos2(x)=sin(x) Note that, sin2(x)+cos2(x)=1

Q: Differentiate the following 1. g(x) = x³ cos x 2. g(x) = 4 sec x + tan x sinx 3. g(x) =- 1+cosx tanx…

A: 1) g(x) = x3cosx2) g(x) = 4secx+tanx3) g(x) = sinx1+cosx4) g(x) = tanx secx5) g(x) = x1+sinx

Q: Prove sech 2  x =1 - tanh  2x

A: we have to prove: sech 2  x =1 - tanh  2x

Q: 3. 1+ tanx tan 2x = sec 2x s*

A: The given identity

Q: (2) elnx = x (1) sin-1x = V1-x2 (1) ax A- Show that : cos x (2) lim x- cosx (2) (1) limx-0 В- Find :

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Q: find integral tan 6 x sec  4 x dx

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Q: Q1) Solve:- 1) lim x-2n 2x-4n 2) lim X(1-cosx) x-0 tan(tan2x)

A: 1)

Q: Find lim Sin 3x (1- Cosx) メーや。 メ*s X Sinzx cosx

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Q: Prove that X -sin 8 2 X sin sin x 8 2 2. 2.

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.