arctan(x) Evaluate dx or show that it diverges. 0, x² + 1

Q: lim sin Zy Fan3y ア

A: Limit y tends to 0.

Q: Evaluate

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Q: +siny+x

A: Side View

Q: Arcsin(x/y) = 4x + 3y %3D

A: Function given is- Arcsinxy=4x+3y We need to determine the second derivative (y'') or d2ydx2 for the…

Q: Integral sign:  cos(lnx) dx

A: According to the given information it is required to calculate the value of the integral:

Q: Integration by Trigonometric Subsituion 10.) x² Arcsin C) dx

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Q: Using Gamma function evaluate xe-3x dx.

A: Given integral is ∫0∞x6e-3xdx. To evaluate the value of integral using gamma function. Formula used:…

Q: sec (In x) + sec2(In x) tan(In x) 2х Given: dx Find: du tan(in x) 2х sec³(In x) + sec²(In x) sec(in…

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Q: DERIVATIVE OF A TRANS FORM 2t Lte sen6t

A: Use Laplace Transform table:   Ltkft=-1kdkdskLft

Q: sin sin A) converges B) diverges

A: Recall: Telescoping Series Test:      Telescoping series are of the form…

Q: xsin x -dx, a > 0. x +a 15. Evaluate by method of residues |

A: Residue theorem

Q: V3x-e2x-(x ln x)(ln(ln x))| In(ln x) Given a function, y = dy Show that dx V3x-e2x (x In…

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Q: Using Beta function, show that dx 3- (b – x) (x – a) |

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Q: terentiation 2 2 Find dy if y=x'+ sinxy 1.

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

Q: 3 5 3-x - dx

A: The given integral is ∫2353-xdx. Evaluate the integral and find whether it is convergent or…

Q: Arc length Find the length of the curve y = In x on the interval [1, e*).

A: Given: The curve y=lnx,  for x∈1, e2.

Q: Reflection: Across Line y = -x YA

A: When a point is reflect across line y=-x then x-coordinate and y-coordinate changes places and also…

Q: Formula, Arc Length = | /1+ [f'(x)]² dx. Where f'(x) denotes the first derivative of f(x). Given the…

A: The formula for the arc length of a function f(x) bounded by the interval [a,b] is: Arc…

Q: converges or diverges explain why? ∫0 to infinity (xe^(-3x))dx

A: The given integral is: ∫0∞xe-3xdx To find the convergence of the integral.

Q: tan-x is dx using integration by parts Find x2

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Q: 2х -3 -dx. Evaluate(x-2)(x² + 1)

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Q: f(x)=\arctan (1-x),[0,1]

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Q: 3. dx Smix-hsxt2

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Q: ‚arcsin(1+x²)] y'of y = In cscya

A: Given y=lnearcsin1+x2cscxWe need to find y'

Q: Partial Differentiation. If u = In(x² + y?) and z = sin-(=), evaluate the following: azu 1. ax azu…

A: Here is the solution of the given problem.

Q: ation (1+xcos 2y)dr-x'sin 2 ydy = 0. %3D

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Q: dx Half-angle Substitution cos x +sin x-1

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Q: chain rule to differentiate the following 1 y = sec 4 sec* (√x + 3)

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Q: Calcu late D X Cos (X) dx

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Q: rpression in r, for x > 0 /9 - x2 5. CSC arctan PACE

A: Let theta = arctan(sqrt(9-x^2)/x)Form there find tan theta

Q: Evaluale lim t+s iHexists.

A: We need to find limt→-1t+1t+1 Now, x=x , x>0-x, x<0 Therefore,  t+1=t+1      , t+1>0-t+1 ,…

Q: 1+ax ). dx Evaluate 1-ax

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Q: tanx - tany = sin(x+y)/cosxcosy

A: The given identity to be proved is,

Q: Ci-2)x OS how that dx = where cis constant of integratron abore or Otherwise Using find f ansurer -2…

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Q: ysiny limy-»o (y+siny)²

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Q: dx Perform a test to determine if converges or diverges. 8 X° +4 dx Does converge or diverge? 8 Vx°…

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Q: Integral Evaluate the √x (x-²) ³ dx

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Q: integral (x-1)sin pie x dx

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Q: lim 0 2 + sin(okr }) k=1 6 O A. J(x + sin(2xx)) dx 6 O B. J(2x + sin(2xx)) dx 3 O C. J(x +…

A: Definite integration limit as sum

Q: sec (In x) + sec2(In x) tan(In x) dx Given: 2x Find: du

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Q: Using Monte Carlo, estimate the value of eTy dx dy.

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Q: 7topic: implicit differentiation

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Q: arctan x dx (けx) It X

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Q: 5. 2х + Зу\ %3 х2

A: Given :  2 x + 3 y 4 = x 2  Find :   implicit differentiation

Q: Bessel fundion Satis fies veyi fy that the Sinx the Bessel equation of

A: We have to verify that the Bessel function J12x=2πxsinx satisfies the Bessel equation of 12.

Q: 3x+2 b. Evaluate dx, using a suitable technique and provide the reason for -2 (3x²+4x+2)* your…

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Q: Partial Differentiation a2z 1. If z = e* sin y + e³ cos x, verify a²z = 0 ду?

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Q: acrsin x:! csc-1 x: arccos x: sec-1 arctan x: cot-lx: : [0, T] :: [0, 플] : (- 1 : (0, 27] :: [-플, 이…

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Q: SVx+sin/x Evaluate: dx.

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Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.