2. (a) Evaluate [ x*V1+4x° dx.

Q: 1- f(x,y) = In(x² + y?) at (1,1)

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

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

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Q: 4. Find the linear approximation to f(x) = cos(x) near a =- [Where L(x) = f(a) + f'(a)(x – a) ]

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Q: du ap B) Prove that dx n- dx v2 where u = f(x) and v = f(x).

A: To find  d(u/v) /dx

Q: e*(1-cos(x)) Exercise: Evaluate S dx.

A: Now evaluate the integral, ∫0∞ex(1-cos(x))xdx Take the minus as outside and it is concluded as…

Q: The critical point of the function* f(x, y) = x² + 5y² + 2 cos x

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Q: (c) Show that (d/dz)z does not exist anywhere,

A: See the attachment

Q: -Find the D.f ofr (x, y) = (x² – y)' at Po(3, 1) with

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Q: If f = 5x2y2 - XY2 then find af at (3,1) %3D dx

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Q: If fCx) is bdd Junchion an f(x) dx = の-3 then 3. True or Fal se ?

A: Solution :- An odd function is defined such that f(−x)=−f(x)

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

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Q: dy Prove that dx of x2 +2x is f'(x)=2x + 2

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Q: Find the linearization L(x) of f (x) = tan x at a =

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Q: Suppose that u and v are differentiable at x = 2 and that u(2) = 4, v(2) = -9, u'(2) = 5, and v'(2)…

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Q: - Find dy at x = -1 if y=u³ +5u-4 and u = x² + x. dx

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Q: یک 2. G(x) = L tanz et et +3 -dt

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Q: Find the linearization L(x)of the function at a .

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Q: If f(x,v) = ex In(5xy) find dy?

A: Given: fx,y=ex2ln5xy. To find: ∂2f∂y2 Solution: In partial derivative we differentiate with respect…

Q: dF find F (x) = J- dx but -x cos(tx) dt t

A: A

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: 3.Find the linear approximation to f(x) = cos x at x, = ÷ and use the linear approximation to…

A: We will use formula for linear approximation.

Q: dy In(5a + 2) Find for y = %3D dx

A: Giveny=ln(5x+2)7e5xdifferentiate…

Q: Find where y(x) is defined by d²y dr? (a) 3x2 – e2, (b) sin 3x + cos r, (c) 1+x – x2 + In r. - -

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Q: If sin(x) f(x)= V2+t2 dt tan(x) and g(y)= f(x) dx g" (4) Then is equal to V5 - 2 V3 - 2V3 11 E- 2V3…

A: Given:            f(x)=∫tanxsinx2+t2dt  and g(y)=∫1yf(x)dx

Q: If sin(x) F(x)= V2+t2 dt /tan(x) and g(y)= dx . g" (4) Then is equal to V5 - 2 V3 2 V3 2 - 2 V3 V –…

A: Given :  fx=∫tanxsinx2+t2dt Differentiating both sides Using Leibnitz Rule, we get…

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: Find the linearization L(x) of the function at a. f(x) = sin(x), a =. 3 L(x) =

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Q: prove that (d/(dx))(sec^-1x)=1/(xsqrt(x^2-1))

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Q: 2. Find whether the function F-(* - y' )i + (v² - 3x)j + (:² - xy is irrotational.

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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

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Q: Find dy at x = -1 if y = u’ +5u – 4 and u = x² +x . dx

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Q: If y = V1-x² sinx, prove that (1–x²) +xy =1– x². dx

A: Given that :- y=1-x2sin-1x Prove that :- 1-x2dydx+xy=1-x2

Q: If y = x tan-x- In /1+ x² then ¬1x-In V1+ x² dy is dx

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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: Find the linearization L(x) of the function at a. f(x) = sin(x), a = 3 L(x)

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Q: 2. Show that the function u = p(xy) + Vxy v(y/x) provides the equation = 0. dy? -

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Q: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of at x = 1. %3D df-1 - dx

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Q: Suppose that f(0) = 1, ƒ(0.5) = 2.5, f(1) = 2, and f(0.25) = f (0.75) = a. Using trapezoidal rule…

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Q: Find the linearization L(x) of the function at a. п f(x) = sin(x), a = 6 L(x) =

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Q: 11) Find a function y-f (x) that satisfies both conditions: d - 6x -4x+5,f(-1) =3 dx %3D dy 2 3 ==+…

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Q: e) Differentiate f (t) = (e-6t+ sin(2-t)) -9- %3D

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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: 1. Use residues to evaluate 1 : xe dx , (a>0).

A: Let fz=ze-zz2+a2 The poles of the function fz are ±ai Choose the contour C consisting of the real…

Q: What is the I.F of (x^2y^3+2y)dx+(2x-2x^3y^2)dy=0?

A: Find the integrating factor

Q: Find dr dy at x = -1 if y =u° +5u – 4 and u = x² +x.

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Q: (1) So“ dx let t=x o Vx

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Q: 3. If f(x) = (1–- t²)e*dt, on what interval is the curve y =f(x) upward? concave

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Q: Solve for x = u + 1 and y = 2u² - 4u d²y dx² with respect to the parameter u

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