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

Q: no 2n? -5 sin( n) d] lim %3D 3. Prove or provide a counterexample for the follow

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Q: 3- y = sec x prove that d? y + y = 2y3 dx2

A: We have to prove the given differential equation to be true.

Q: Let ro)-플-x a-글 FW) = b = 0, and n=3. Then: cos (f(x))dx =

A: We can find the integration as below

Q: -3 Evaluate: ²¹²² ²³ y cos(z³) dx dy dz

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Q: () -1 -3y If f(x, y) = tan %3D then find fr .

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Q: 1. If y= tan x, prove that y"= 2(y² +1)(3y² +1).

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Q: et – 12x + I lim r4 +1 e* +1 lim 1H00 I - 2 lim sin

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Q: f(1, y) = cos cos y is = COS I COS y

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Q: b) f(x) = cosx on the interval [0,] %3D

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Q: if y=tan x,prove that y'''=2(1+y²)(3+y²)

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Q: 1. If y= tan x, prove that y``= 2(y² +1)(3y² +1).

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Q: 3e2* -1 d) lim 2x 4e* +cos x

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Q: pin z +y 12 + cos 2 2r F(1,y, 2) =- TY + 2,- + Cos 2

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Q: 1. D'y+y=sec x² 2. D'y+y= tanx

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Q: y= (1+x?)tan x- x? y' = 1 + xtan1-2x y' = 1 + xtan -2x y' = 1 + 2xtan 1-2x y' 1 + 2xtan -2x y'…

A: In this question we are required to calculate the derivative of the function.

Q: 2.xy x² – y? Show that - = 0 if z= Tan

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Q: (c) 1 lim – cos(6r) 5x

A: Explanation of the solution is given below...

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: (tan y+2)dy cos y4-9 tan² y -9tan

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Q: 4. What is the domain of y = - cos x? А. 4 В. 3 C. R D. [-1,1]

A: The cosine trigonometric function, y = cos(x) is defined for every real x i.e R.

Q: For cos2(xy) = L. For cos2(xy) =-, evaluate y' when x = 1. 4 3

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Q: Find y' cos(xy) - y^4 = 5 - 3x

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Q: 1. ( )f So y sin(ry)dydr

A: Integration of sinx is -cosx

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

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Q: dz (2) Suppose z is a function of x and and suppose cos(32) xyz?. Find in Y, terms of x, y, and z.

A: The given function is, cos3z=xyz2

Q: 2a? sin(y) lim (x ,y) → (0,0) 2x2 + 4y2 Evaluate Use DNE for does not exist, oo for infinity or -00…

A: Given limit, lim(x,y)→(0,0)2x2sin(y)2x2+4y2

Q: If y = tan x, prove that y``= 2(1+y² )(3+ y²).

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Q: a2z a2z dz Q3) A: If e-(sinx + cosy), show that ax2 ду? at

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Q: 2 dx 5, is same as evaluating lim cos C+2+ F(<x))". Determine the value of f(x) if x=3.22 In…

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Q: -1 tan y2 y2 +1 n¬² y tan-1 y ) dy

A: We can integrate this integral by using the integration by substitution technique. Here we have to…

Q: fCx) at c0,2) で +x + co.2) 2. メ 2/3

A: Given curve is fx=23x2+x+2. To find the equation of tangent line and normal line of the curve at…

Q: xy' – y = x cosx, with y(7/2)= .

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Q: 2-+x* cos y = 0 dy y

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Q: If y= tan x , prove that y`= 2(1+ y² )(3+ y²).

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Q: 2+X y = Arccot x+ Arctan 1-2x

A: To determine the derivative of the the function ; y=Arccot x+Arctan2+x1-2x Differentiate both sides…

Q: t+1 e i+ sin 2t lim 花1=?

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Q: ∫sin^6 y cos^4 y dy, limits from 0 to pi/2

A: Consider the definite integral ∫0π/2sin6y cos4y dy to solve this integral, use the below reduction…

Q: dy is: If y = tan(47x²) then dx

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Q: 13. ebx cos x dx exists only when b < 0. lim t→∞

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Q: tane Q2) a) Find " sec²y dy dx

A: Given : ddx∫0tanθsec2ydy

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: 2U y'sy tan(x) 2) yy's 2Xes

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Q: [x 2. x tan --yjA +xdh = 0; when x=0, y=z/2 ......

A: Given differential eqution  x tan2yx-y dx +xdy=0      ;  y0=π2

Q: II. f(t) = cos t, lim h

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Q: -5t i + j+ sin(3t) k sin (t) lim e t 0

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Q: lim-sin t t0 In(2et_1) %3D A © D B.

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Q: IF X = Sect ,y=tant evaluate dy イxと %3D

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

Q: Q.1 Determine a, b, c, d & e such that cos ax + bx+ cx + dx + e 2 lim-

A: To find the values of a,b,c,d and e