True or False y = tan¯1 x if and only if x = tan y, where –o < x < ∞ and -< y <

Q: sin? 0 sin 2x tan´ x 2. limøseco 3. lim 0→0 1 – cos 40 4. lim- x→0 sin 3x 5. lim -

A: Solution

Q: 14. Find the smallest positive root of tan x+2 tanh x = 0.

A: Newton Raphson Method:- The root is xi+1 =xi - fxif'xi; i=0, 1, 2, ....   Given equation is tanx +2…

Q: 1- cos x The lim X40 sin x is equal to O 2 Zero O-

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Q: 23 Example 49 Let f(x)= sin" x-cos" x and g(x)=1+ tanlx1. Then, the number of values of x in…

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Q: iV. Prove that tan50 t5-10t3+5t where t tan0. Deduce the values of 5t4-10t2+1 tan for n 1,2,3,4.

A: Consider the given information: To prove that tan5θ=t5-10t3+5t5t4-10t2+1,   t=tanθ

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

A: Topic = Limits

Q: 2. True or False. The dx [Arctan(tan x)] = 1 for all x in the domain. ans. True

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Q: 1. lim 3" 5. lim tan r 2. lim 5 6. lim cos r 3. lim log r 4. lim cos r 7. lim sinr

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Q: The largest value of the non-negative integer a for which lim x →1 - ax + sin(x - 1) + a x + sin(x −…

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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: If y = sin x, then y' = - cot x sin x - tan x sec x sec x -sin x - Cs X tan x cos X CSC X

A: Given function is y=sinx. Differentiating the given function with respect to x, we get…

Q: CianXtl) 2 tan x 8. Prove the identity: sin 2x = 1+ tan x L.S. es

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Q: 12) Solve: (tan x) (2cosx+1) = 0 %3D tan x = 0 2 cos x + 1 = 0 x = 0 2cos x = -1 m<x= 0 coS X = - m<…

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Q: 11. y = coS x COS X -2 tan x 12. y = x? sin x tan x 13. у %3D 1 14. y = --3 sin x 15. y = x cot x

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Q: 1 lim is equal to: (t – 1)2 '

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Q: - Ix-4 5. lim 1 3x² +5x+2 6. lim 14 x -x-12 tan 0 cos 20 7. lim 0–→0 sin 20 8. lim 0→n/2 tan0

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Q: 12 If sinh x= find cosh x, tanh x, coth x, sech x, and csch x. 35

A: Given, sinh x = 1235   We have to find  cosh x, tanh x, coth x, sech x  and  csc hx

Q: Prove the identity. 1+ tanh(x) = e2x 1- tanh(x) 1 + cosh(x) 1+ tanh(x) 1- tanh(x) 1 cosh(x) cosh(x)…

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Q: True or false: If tan 3x = any integer n. + nn for 4 1, then x = %3D

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Q: (-등, 풍) satisfying TT Find all values of 0 in the interval 2 2 2 the equation (1 – tan 0)(1 + tan 0)…

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Q: 22. lim cos2 (x - tan x) cos 2x - 1 sin x 24. lim

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Q: 6. lim 3**1 16. lim sin 9x 7. lim 2-1 17. lim 0 sin 10x tan ax 8. lim In(x +x - 1) 18. lim 9. lim…

A: 6. Given the limit limx→-13x+1 The limit is defined at x→-1 Therefore the limit value at x→-1.…

Q: 1+sin x sin x <x<0 6 -- If f(x) = {b , x = 0 is continuous at x = 0, find the values of a and b. tan…

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Q: Infinite limits at infinity Determine the following limits.

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Q: In Problems 7–16, use a table to find the indicated limit

A: The given expression is limx→24x3

Q: Solve 2cos (x)- sin(x)=2 exactly for all x in the interval [0,27).

A: 2cos2x-sinx=2⇒21-sin2x-sinx=2…

Q: 2/2 and <x< 3 Зл find tan 2x. 2' 4. If sin x

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Q: 1. If tan z = - 0.5 then tan( – æ) - 2. If sin z = 0.5 then sin( – æ) = 3. If cos a = 0.2 then cos(…

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Q: x² +9 √(x² - 1)(x^² + 4) In 1x + 11 + In |x-1| + tan-¹) + C Option 1 In x +11+ In |x-1|-tan ¹ () + C…

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Q: If 1, = | x" sin x dx, prove that 1, = nx"-! evaluate -1,. sin x- x" cosx– n(n-1)I, 2. Hence, = NX…

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Q: TT True or False tan 0 • cos 0 sin 0 for any 0 # (2k + 1) %3D

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Q: 1. Find (a) sin(x + y), (b) cos(x + y), (c) sin(x – y), (d) cos(x – y), (e) quadrant containing x +…

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Q: 2.2 Find all values of x in the interval 0<x< 2n for which -< sin x < 2

A: Given that -12&lt;sin x&lt;12.…

Q: a. Show that y = tan u increases on every open interval in its domain. b. If the conclusion in part…

A: y=tanu Differentiating with respect to u, we get dydu=sec2u Now clearly, sec2u≥0 for every value of…

Q: x² + 9 dx J x2 – 1)(x² + 4) | In \x + 1| + In |x – 1| +; tan-1 (-) + c -In |x + 1| - In |x – 1| -;…

A: Topic:- application of integration

Q: sin 0 – cos 0 lim 0→x/4 tan0 – 1 2(cos x)2 + 3 cos x – 2 lim 2 cos x – 1 y In y – y lim y»e In(y5) –…

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Q: tan (x) J Cos cos“(x) 하an7(x) + 늑tan®(w) +C O tan'(x)7tan?(x) +9]+ C tan7(x) 36 O sin…

A: Here we have to integrate the given function.

Q: 1-To find the smallest positive root of tan x-x=0 which of the following re-arrangement is…

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Q: 4. For x near zero it is possible to write tan x = 1+ 0(x") and tan x = 1 + o(x°). Find the values…

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Q: 1– tan(*,) [1– sin x] lim 1+ tan(x (¥2) [z – 2x] x- - 2 1/8 1/32

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Q: 1- tan lim 1– tan(*,) [1– sin.x] sin x] (2, x→| (¥2)[[7 – 2x} n – 1+ tan(x 1/32 O 1/8

A: The given expression is limx→21-tanx21-sin x1+tanx2π-2x3.

Q: Example : Find an approximation to zero of tan(nx) – 6 = 0, in [0, 0.48]by Secant Method.

A: To approximate the zero of f(x) using secant method.

Q: 2 and 3 Suppose that tan 0 <0<T. Find the exact values of sin and tan JT sin 2 = Undefined tan 2

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Q: (1) limr-(n/2)-(tan x)cos x (2) lim,-o x-3(tan-x-x) (b) If у %3D 4u?-Зи + 2 %; и 3 е* + 2e2х, find…

A: For other questions reupload according to bartleby guidelines

Q: 1. Evaluate 2. Evaluate sin(20) 30 x-2x cos x sin x limo lim, 0

A: Given is  limθ→0sin(2θ)3θ. L'Hospital rule: limx→af(x)g(x)=limx→af'(x)g'(x) NOTE: According to the…

Q: cos x 13. lim x-(7/2)* 1 – sin x e21 – 1 15. lim - -0 sin t 1 - sin 0 17. lim 0/2 1 + cos 20

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Q: Problem 1. (a) Show that that 1 – tanh² x = sech² x and use it to prove that sech(tanh x) = v1 – x².

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: a. Show that y = tan u increases on every open interval in its domain. b. If the conclusion in part…

A: (a)  Given,

Q: 3. Given f(x) = cot(x) sin(x) and g(x) = cos³(-x)(sec² (x)-1) sin² (x) a. Prove that f(x) = g(x).…

A: Given that,  fx=cotxsinx and gx=cos3-xsec2x-1sin2x