Find an antideriuative Flx) of the functian f(x) = 8 sinx such that FlO)=D1 %3D 13 + COSX

Q: Q2/ Prove that 1 dx = v2 Jo 1+sin(x)

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Q: 2x cos(2x)dx

A: Given : ∫2xcos2xdx

Q: If the substitution u = x/2 is made, the integral 1-(플)2 dx = %3D -

A: Let's integrate.

Q: Use Fubini's Theorem to evaluate .2 -dx dy. I + xy

A: Given :            ∫02∫01 x1+xy dxdy By Fubini's theorem, the above integral can be rewritten as ∫01…

Q: Find dy for all of : dx 1- y = x/Inx у

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Q: Calculate by u- Substitution, the follo wing integral definite 3 • cos x • sin x •dx

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Q: The linear approximation at z = 0 to sin(8x) is A + Bx where A is: %3D and where Bis:

A: Given : The linear approximation at x=0 to sin(8x) is Ax + B   To Find : Value of A and B

Q: Find d3f where f(x, y, z) = ln(x + y − z) + cos(x2y)

A: As per the question we are given a multivariate function as : f(x, y, z) = ln(x + y − z) + cos(x2y)…

Q: Evaluate the integral. cos y dy sin 2y + 2 sin y – 3

A:

Q: Use Green's Theorem to evaluate the line integral. ex cos(2y) dx – 2ex sin(2y) dy C: x2 + y2 = a²

A: Use Green's theorem

Q: Use (a) the Trapezoidal Rule integral 1to 4    cos  2  x dx                 with n= 8

A: Given Data The integral is . The number of intervals is n=8.   The function of the given integral…

Q: Find Fxx and Fxyz of: XX хуz y2+Cos (xz) f (x, y, z) : 2 Siny

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Q: - Sva cos 2t dt from x= 0 to x= Find the length of the curve y =

A:

Q: Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); fi-) U =

A: we can solve this as follows:

Q: Find a result by using exact for (sinxcosy)dx = -(cosxsiny)dy = 0 b. (x-6xy + y² + 10)dy = -(x² -…

A: I am attaching image so that you understand each and every step.

Q: Evaluate the double integral: sin(y) /y³ dy dx.

A: Change the order of integration to simplify the integral .               Disclaimer: Since you have…

Q: 3. Linear DE of Order one 2y(у? — х)dy %3D dx

A: Linear equation of dx/dy form is made

Q: HW 0 1f y=tanx show thats y" = -2Siny Cosy %3D

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Q: dz is equal to .. dt Let z= In (x2+y²) where x=ue"sin t and y = ue"cos t. If u= -2 and t=0 then -

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Q: d²y 1.) of y = sinInß and x = In(Inß) dx2

A: Topic = Derivative As per guidelines , At a time only one question can be answered out of different…

Q: (x,() + x(x, t) = sin(t) u(n, 0) = cos(7), at %3D %3D nER.

A:

Q: ().小) of af f(x, y)=sin 1+y, +cos %3D %3D X +1 s215 ||

A: To find The partial derivatives of f(x,y)

Q: Evaluate the integral arcsin a dx. 1- a2 x arcsin x + C 4 + C Væ2 – 1 + C V1 - a? O x arcsin a + V1…

A: We will use Substitution and then Integration by parts

Q: Compute cos(x) cos(y) dx – sin(x) sin(y) dy, where c(t) = (9t, 4t2), o sts 1. (Round your answer to…

A:

Q: Q5. Evaluate the triple integral cos(y²) dz dx dy.

A: The given triple integral is;  Cos(y2), z from 1 to 3, x from 0 to y, y from 0 to sqrt(pi/2).

Q: Where is the function f(x, y) = e' arctan (VI+In(x+y)

A: In this question, the concept of continuity is applied. Given function is fx,y=etan-11+lnx+y

Q: e ln (xle) (2– sec²r)cm#/c°sec³x sec(3A – x) What should be the value of A for -dx to be integrable…

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Q: Find the length of the curve y = V cos 2t dt from x= 0 to x = 4

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Q: Find dy/dx for the following: 6. (sinvx csc Vx) 9) y* = sin-1 x 8) у%3D 10) y = xtanx + sin-ly 11)…

A: Solution: Hey, since there are multiple questions posted, we will answer first question. If you want…

Q: Q5. Evaluate the triple integral ²³ cos (y²) dz dx dy.

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Q: Find if y%3D cos (2x)+ 2еж: dx dy

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Q: Find the potential P(x,y) attached to the exact ODE 2x sin(y) +x² cos(y) y' = 0

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Q: Use Simpson's Rule e with n=10 Y: X Sin (x), OSXS 27

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Q: 2- is the D.E:(3x² + y cosx )dx + ( sinx-4y )dy = 0 | a- - Exact b- linear D.E (show that)

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Q: Evaluate the integral. V16-a? 1 dy dx dz = -V16-x2 (x2 + y?)1/2 -4.

A: We can solve as follows

Q: Calculate the double integral. 9x sin(x + y) dA, R = 9v 3

A:

Q: b) Differentiate y = e (In3x) + tan (3y) with respect to x. %3D + 2e In 3x Ans: dy %3D 3 1-

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Q: Evaluate the integral. * T/2 sin³x cos y dx

A: Using identity         Sin2x+cos2x=1

Q: 7. Calculate dy/dx at the point indicated: f(0) = (7tan O, cos O), 0=/4

A: Here we will use the concept of parametric equation and Derivative of parametric ewyations

Q: Use Green's Theorem to evaluate the line integral. et cos(2y) dx 2ex sin(2y) dy C: x2 + y2 = a?

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Q: Find dy/dx: (a). y = cos 8x + sin r2, (b). y = Vcos 8x + sin x². %3D

A:

Q: Evaluate the triple integral 5 z sin x dy dx dz 3.

A: Given:

Q: Evaluate the double integral: cos(y') Vy3 dy dx.

A: The solution is given as

Q: Find f(x)

A: We have to find out

Q: Calculate the Cauchy principal value. 8 COS X V.P. Leta -dx, (a > 0). (a²-x²)

A: We solve by using residues.

Q: Find the total differential. z = e4x sin(3y) dz =

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Q: Complete the integration: Ssin (x)cos (x)dx = sin (2x) sin (2x) + C ? %3D 16 32 Determine the yalue…

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Q: Show that g(x) = cos 2 =x+3 ™K(x, t) g(t) dt 0 || sin x cos t, 0≤x≤t Y sin texr

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Q: Find the intergral of  (t^2 sin(t)cos(t) +t sin^2 (t) )dt

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Q: Find the general sebution of the oDE dy Sin(x+y)+ Cos (X+y) %3D dx

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: