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

Q: Q2: Find the 1. y = 1- 2. y [In(x² + 2)²]³ 3. y = xcsex tan² (cos x) 4. y for the following…

A: As per guidelines we can answer only one question at a time, so if you need more answers kindly…

Q: e sin r – x lim 4 cos a – 4 O 0.2500 O - 0.2500 0.5000 O 0.5000

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Q: T sin(x) cos(x) dæ = Hint:

A: Topic:- integration

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Q: e) y = In(cos 4 x) f) y = sin² x y = In(cos(e3*)) g)

A: We can solve using first order differentiation (using chain rule)

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A: Given:  A)∫0elnx2dx=limc→0+∫celnx2dx B) None of the given choices C) ∫05dx25-x2=limc→5-∫0cdx25-x2 D)…

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Q: #1: Given: y = cos (x

A: Given trigonometric  function y=cosx-π2

Q: Hiw/ Find F'(x) 1. if F(x) = x, tanx 2-if y = Sinx it casx 3- Find g" ()if y co) = Sec y ex) g ex)…

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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: -2x 39. lim (e* cos x)

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Q: dy 4. If y = tan-1(cos x), then dx - sin x А. 1+cos? x B. -(sec-1(cos x))² sin x C. (sec-1(cos x))?…

A: If y=tan-1cos x, then we have to find dydx.

Q: If y = tanh"(k/x) and x (1 - 144x) y'=A Then A= .

A: First we find the derivative of the given function y.  After that we substitute k=12 in the result…

Q: sec x-cos X lim equals (A) 0 1 (B) (C) 1 (D) 2 (E) none of these

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Q: 4Find dy/dx for: y = sec?x - tan?x b- y = sec -x) C- y = sin(tan(3x))

A: Since, you have posted multiple questions and the questions marked by you has multiple sub parts ,…

Q: 2) Use the figure to give approximate values for the following (if they exist). Enter your answer as…

A: The above figure shows the graph of function f(x), find the following: (a) f(1)(b) lim f(x)x→1(c)…

Q: 2y-n -Tt 7. lim cos y 2

A: Given:         limy→12π2y-πcos y    Let   π2-x=y, ⇒π-2x=2y      As y→π2,x→0

Q: If 1 1. f(x)dx = n(x) - tan(x) - 4² + x² + 6x + 0 4e C 3 then find f(x)

A: We can find f(x) as below, by finding the derivative.

Q: 4х — Зу y? sin? x - lim (x,y)→(0,0) 2x +3y (b) lim (1,4)→(0,0) x²(y² + 1)

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Q: * /Q3 e*-(x+1) lim X→0 CoSx-1 %3D -1 1 -2 O O O O

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Q: d) S x?cos (x) dx 2 a) Find f' given that f(x) = cos' (3x+1) %3D sin3x-sin 6x b) Evaluate lim x-+0

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Q: Which of the following is equal to lim h→0 Old + 1/1/12 2 dx +=h { (20²2 +20)] - [2²] + d [1 dx da 2…

A: This is a problem related to differentiation. Based on the definition of differentiation we will…

Q: c) f(x)=tan(cos².x) 11 COS X 1+ sin.x Dy=- b) y = 2

A: e)  f(x)=tan(cos2x)  f) y=cosx/(1+sinx) g) y=ex^2/x3 Repost the next part.

Q: 2x² sin x + 3y³ lim (x,y) →(0,0) 3x³ + 2y² if we approach along y-axis, we will get 0. Select one: O…

A: To determine whether the following statement is True or False.limx, y→0, 0 2x2 sin x+3y33x3+2y2if we…

Q: Find values of a and b for which cos (ax) – b -1. lim x→0 2x2

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Q: 1 x" cos (nx)dx 1+n? Evaluate lim

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Q: I sec25x dx = ? tan x +C 1/5 tan x +c 1/5 tan 8x +C

A: We will solve the problem

Q: Which of the following is equal to f(x)dx where S(x) =- sin(x) if 0<x< a/2 l cos(x) if 1/2<x<a } -2

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Q: (D' + D)y= tan x. Ans.: y =C +C_cosx+C_ sinx-In sin x- sin x.In(sec.x+ tan x).

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Q: If f(x) is continuous and ∫ 2 0 f(x)=dx=6  then evaluate ∫ pi 2 f(2sin θ) cos θ dθ

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Q: 1 lim (a2 + y?) sin (2,y) (0,0) x² + y2 Select one: O True O False

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Q: h(x) = x – sin x for 0 <x < 4A -

A: Given the h(x)=x-sinx for 0≤x≤4π We need to determine: a)the intervals of monotonicity for the given…

Q: tan(хy) = ? lim %3D 2. (х,у) ->(0,1) х*у+x (a) 0 (b) (c) (d) (е) 1 -12

A: We have to find the value of the given limit: limx,y→0,1tan xyx2y+x The given limit is 00…

Q: - ysec?x and y = 5 when x = 0, then y = etan x + 4 A в etan X + 5 5etan x D) tan x+ 5 E) tan x+ 5e*

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Q: Q2) A: If u = sin-()+ tan-(), prove that du ди x=+y дх ду = 0 ax ay n lim (1+ (1 + iV3)10 B: Find:…

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Q: y? lim y→0 In cos y Оз -2 O O o O

A: To find: limy→0y2lncosy Concept used: Apply L' hopital rule if the output is in the indeterminate…

Q: F(x)= in for -くX (X) =<osXfor os:X いゴ, and h(x) = tan x for <x<I. Find each of the following…

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Q: a) cos(xy)=2y, find y' DI y = cot-1 1+x 1-x

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Q: f(x) = sin x and g(x) = cos x if x= 60° %3D find [g(x)] O 1/2 O 1/4 O 1/4 O -1/2

A: Topic- trigonometry

Q: tan (xy) =D? lim (x,y)→(0,1) x´y+x (a) 0 (b) (c) (d) (e) 1 1/4 1/3

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Q: Q2) a) Find f xein(x²+5) cos(x? + 5) dx

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Q: sec x + coOS x dx 2 cos x

A: To evaluate

Q: Q3// Answer the following (20 mark): А. Vx+5-3 1. lim x-4 x-4 x+x cosx 2. lim x-0 sinx cosx

A: