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Q: e Divergence Theorem to evalu (4x + 10y + z²) dS Js

A:

Q: Differentiate fx) with respect to g(x) of yx= xsiny

A: To find the derivative

Q: (b) lim (z.y)→(0,0) Vr4 + y3 +1–1

A: limit of the rational function

Q: du -xy du Ifu =f(x² +2yz,y² +2zx) Prove that (y- zx)-(x² - yz) -NX ду

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Q: Vhich of the following is correct? A) dx = lim | 1 %3D xp- = lim 4 V.r+4 V.r+4 V.r+4 -2 V.x+4 B) S…

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Q: If f(x) = A B C -S sec²x D tanx l+et sec 3x √1+1² 1+e' 1+e lanx -dt, then f'(x) equals tanx 1+e In…

A: The Leibniz integral rule gives a formula for differentiation of a definite integral whose limits…

Q: (b) Integrate f(x, y) = 4e0.8x - 0.5y using h = 0.5 with y(0) 2 from x = 0 to 0.5.

A:

Q: 2t dt = 1 – t4 lim x→1- A) B) 2 C) 0. D) 1. 1

A: Given limx→1-∫0x2t1-t4 dt

Q: 2. Show that 4=x i+y°j+:'k is irotational.

A:

Q: t² + 1 t 1 %3D lim→1- h(t) = ?

A:

Q: ¸(1+ h)² −1 lim h→0 h using the squeeze Theor

A:

Q: 2. Find frxz for f(x, y,z)= z² e³xy

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Q: -8 6. Evaluate the integral +y² dydx

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Q: Find the Linearization L(x) of y = (1+x)¬1/² at a = 8. L(x) = %3D

A:

Q: limx→o (t+1)f(t)dt Assume f (0) = 4 %3D 3x2

A: Explanation of the answer is as follows

Q: Compute 1 t2 – 4t – 21 dt. lim 27 (x – 7)2

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Q: f(x, y) = In (x²y - x) %3D

A: Here, the given function is: f(x,y)=ln(x2y-x) First to find the first derivatives:…

Q: Suppose F(x,y)=sin²(xy +e"), where x=u² +v and y = In(u² +v). Find the . ƏF ¸ ÔF value of when u =1…

A: The given function is: F(x,y)=sin2xy+eywhere:x=u2+v         and         y=lnu2+v

Q: Find the solution (varition of parameter)   X2y11-2xy1+2y=x3sin x

A: According to the given information, it is required to find the solution of the given differential…

Q: 3y +5xy + 2x lim (1) (z3-2) 3y +2.xy 4(x*-y*) (i) lim (10 x -y +1-1 lim (1.)-0.0) (Hint: use…

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Q: 6) If y=x² +1+ f dt , prove that y"= 2 - x2

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Q: 1. a- Find a result by using variable separation for ý=secy h- xy = x + y

A:

Q: Find y(0.5) for y'=-2x-y, y(0) = -1, with step length (h= 0.1) using Runge-Kutta.

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Identify the removable discontinuity. x² – 1 f(x) : X- 1 (х, у) %3D Additional Materials

A: A removable discontinuity is one at which the limit of the function exists but does not equal the…

Q: xsin 1x Vx+1 2tan-x Vx+1 2tan-1x QI) Find of y=: e2x+1

A: We will find dy/dx as following .

Q: 4. F(x) = (1- t) dt %3D 4

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Q: (a) x² + zsen xyz = 0

A:

Q: If y(t) solves the IVP dy = y2021 y2019 y(2021)= -2019, dt then lim y(t) is: t- 00 Oa. 1 O b. 00 O.O…

A: Given differential equation is dydt=y2021-y2019.       ........1 It is an autonomous differential…

Q: : Find y(0.5) for y'=-2x-y, y(0) = -1, with step length (h= 0.1) using Runge-Kutta.

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

Q: - Find the total differential df of f (x, y) = (x² + y²) 3/2.

A:

Q: lim, - „f(x) = 0, then fx)dx diverges Select one: O True False

A: The given statement is

Q: lim, f(x)= 0, then | f(x)dx diverges

A: Statement:  limx→∞ f(x)≠0,  then ∫1∞ f(x) dx   diverges.

Q: Q2- If Z = f(x, y) = sin(x³y5) Find fyy and fyx

A:

Q: 23. lim Vx2 + y² In(x² + y²) (xy)→(0,0)

A: This question is related to limit in two variables.

Q: 3.2 Let f(x) = Approximate the integral x4 x L f(x) dx using the Trapezoidal rule with n = 4. -2

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Q: (ii)If y=(x+Jx* +1. prove that y'= Vx +1

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Q: ecos a tan(z+ x) 2x – y+ z V4x2 + y – z xyz T T T x + 2y + 3z 3x + 4y – 2z, x + y + z

A:

Q: ) Fnl the Vdume of the Selid enclesed by the curres "about the x-axS. y=e^, y=0 x =©,'x=/

A: To find out the volume of solid of revolution.

Q: In (secx) a) | sec2t dt + cot x

A:

Q: If ƒf (x) =¸ (A) (B) Sº sec²x 1+elanx In (secx) √✓ 1+tan²x tanx 1+e sec ³x tanx 1+e 1+1² tanx…

A: Using Leibnitz integral rule.

Q: a) Use the definitlon of derlvative to find ds If dt 2t+1

A: As per bartleby guideline for more than one question asked only first is to be answered please…

Q: Let y : R → R be the real-valued function defined on the real line, which is the solution of the…

A: The differential equation is given as Y’  = -xy + x , y(o) = 2 From the type of the problem we can…

Q: Q9. Find y2 using Reduction of Order y" – 3.ry +4y = 0, Yı 1 = x?

A:

Q: Find the 2nd solution using reduction of order. xy" +y' = 0; y1 = Inx For the toolbar, press ALT+F10…

A: Just I have used the method of reduction of order and solve in detail and find that  Second solution…

Q: Evaluate xsec¬xdx using integration by parts. OA x2 -sec-1x-(x² – 1)3/2+c 2 O B. x? 1/2 2 Oc x2…

A: