(sin(x² +y²) ²+y² if (x,y) # (0,0) (ii) Check continuity of the function at (0,0), if (x,y) = (0, 0

Q: f(x) = { cos x, xpi  which lim does not exist

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Q: 1. Find the tangent line to the graph (4-x)y? = x³ at the point (2, 2). 2. Find the tangent line to…

A: Equation of tangent line

Q: a) Find the directional derivative of a(r, y) = 3-y at (1, 1) in the direction (-3,4). b) Find and…

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Q: x=2- secy, x=2, y = 3 and y = 0; about x = 2

A: Using Washer method, we find the volume of revolution of the given region. The formula is for the…

Q: Find the absolute extrema of the function on the closed interval. y = 5ex sin x, [0, π]

A: Solution:-Given functiony=5exsin x in [0,π]∴f(x)=5exsin xf'(x)=ddx5exsin x∴f'(x)=5ex cos x+5ex sin…

Q: cos x dx - In (1 +x) 1- cos x a) b) lim

A: Given: a)∫011-cos xx2dx b)limx→0ln1+x21-cos x

Q: lim (x.y)-(0,0) cos( x² +y2 (x, y) # (0,0) f(x, y) = (x, y) = (0,0) %3D is continuous at (0, 0).

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Q: az QI. Find the az and ax partial derivative ду x² sin (y*) + xe³ – cos (z) = 3y – 6z + 8

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Q: { 1/(x + 2) , x2 , sin(x – 1)/(x - 1) , x 1. y = F(x) =

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Q: 1 (a) Use partial differentiation to determine the expressions for 2 in the following cases: ) x +y…

A: Here is the solution

Q: x sin if x # 0 Show that the function f(x)= is differentiable at x = 3D0 and f '(0)= 0. if x = 0

A: A  function is  differentiable at  point c if L f'c=R f'cwhere L f'c=limx→c-fx-fcx-c   =left hand…

Q: lim (x,y)¬(0,0) cos-1 (*-xy x²+y²

A: Given

Q: 9) Find all relative extrema in the interval (0, 2π) for y = x - cos x

A: Here we have to find the relative extrema.

Q: G. (CHAIN RULE) 1. f(x) = (3x² - 2x+4)² 2. y = sin 2x 4 (a² - y²)² 4. g(x)= (3x² + 4x - 5)5 3. 2 =

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Q: Find the absolute maximum and minimum values for f(x, y) = 5 sin(x) + 10 cos(y) on the rectangle R…

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Q: tan x + i tanh y 1- i tan x tanh y 18. tan z = tan(x + iy)

A: We have to prove

Q: lim (x,y)→(0,0) r sin² y + y sin² a x² + 3y²

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Q: 3.44 3. Test for homogeneity f (x, y) tanx-sec²x - cosy

A: Question : Test for the homogeneity f(x, y) = tanx - sec²x - cosy

Q: 4. Interval 0<x<n, function, f(x) = sin 2x. %3D

A: We have to find the Fourier series of the function fx=sin2x ,x∈0,π

Q: The second partial derivative 2) {(**3)= e In y ė In g %3D 2, 2 In -a)+(9-b)

A: We have to find the second partial derivative of the given functions.please see the explanation…

Q: az Q1. Find the az and ax partial derivative ду x sin(y') + xe – cos (2²) = 3y – 6z + 8

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Q: Prove the reduction formula

A: To prove: ∫tankx dx=tank-1xk-1-∫tank-2x dx

Q: ..LH.S.-R.H.S. - HW/ Prove that: (1) 1-tanh x=sech'x

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Q: -2,2] R, then show that the function sin for x 0, f(x) = for x 0, aly continuous.

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: f(z) = cos (z - 2). where f' (x) =- sin(z - 2) f (1) = zei,where f' (x) = ei-zei f(z) = z - 4r - 2,…

A: Given:- f(x)= cos (x-2), where f'(x)=-sin(x-2) f(x)=xe-x/2 where f'(x)= e-x/2 -0.5xe-x/2…

Q: Test for homogeneity 3. f(x, y) = tanx - sec²x - cosy 4. f(x, y): x²+3xy

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Q: slope of the line tangent to the curve cos(5x-4y)-x(e^-x)=(-7pi/2)*(e^(-7pi/2))at the point…

A: To find the slope we need dy/dx We differentiate both sides of the given function with respect to x.…

Q: lim cos x + x cos a. 0 b. 1 d. does not exist

A: This question is based on Squeeze theorem.

Q: Q4 1-F(x)=limx→0 vV(x2+3)-3}/x2 2- limy 3y+5y2-7 10y3-11y+12 sin4x 3 - lim 0 sin2x

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Q: Limit -1 to 1 integral (1-1/2 x) dx

A: Given:        ∫-111 - 12x dx   To find the value of ∫-111 - 12x dx   Formula:          ∫xn dx = xn…

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: uy constants. Show that lim,y(t) = 0 for every solution of this equation.

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Q: II. Derivatives of Transcendental Functions. 6. y = x²e 7. y = 52x+1 8. y = In|sinx| 9. y = xlnx – x…

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Q: tanx -√ S sec²x 1+ et tanx In (secx) √✓ 1+tan²x 1+ elanx sec ³x 1+etanx If f(x) = A B (с 1+1² 1+e'…

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Q: Differentiation [SND] If y = (r+ v1+x²)", prove that, (1+2²) 2 +ry - m²y =0

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Q: Find the limits

A: Consider the provided expression, limx,y→0,4xy Find the limit of the provided expression.

Q: A function x x(y, z) is defined implicitly by the equation 2 x4 + 2 y4 +3 x y z+z² = 0 Use implicit…

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Q: 6. Given f(x,y)= %3D y a) find the directional derivative of f(x,y) at (1, -2) in the direction of…

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Q: Method of differentiation. 19. Solve (1-x²) dy − xdx + m²y=0 - where x = 0, y=0, x=m dx

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Q: tanx If f(x) = (Α) B C D S 0 sec ³x 1+etanx In (secx) √ 1+tan²x tanx 1+e sec²x 1+ etanx 1+1² -dt,…

A: Here, given that: f(x)=∫0tan x1+t21+etdt...(1)

Q: 2. Find the directional derivative of f(x, y) = -2e* cos y at %3D (0, ) in the direction of v = (-6,…

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Q: |(y) + (0,0) (x. y) (0,0) Show that the function f (x, y). is continuous at the origin however =…

A: consider the equation  f(x,y)=∑xyx2-y2x2+y2 ,0  x,y  #(0,0)xyx2+y2 where f(0,0)

Q: tanx If f (x) = A (В) (ⒸC) D - St 0 sec 3x 1+ e tanx In (secx) √ 1+tan ²x 1+ e tanx sec²x 1+elanx…

A: Finding the derivative of the integral

Q: sin(2x3 +3y3) If f(x,y)= 5330x2+2665y2 (x,y)# (0,0) then (x,y)=(0,0)

A: Given,             fx,y=sin2x3+3y35330x2+2665y2x,y≠0,00x,y=0,0

Q: 2. Use suitable linearization to find the approximate value for the function at point P. f(x,y) (x-…

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Q: 4x5-x*y2-2y5 12x5-6y5 Define the function f (x,y) = at the origin so that it becomes continuous…

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Q: separable 9-X(2lnX+1) Sin y+ ycosy

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Q: lim(x,y)-&gt;(0,0) = (1+x2+y2-cos(x2+y2))/(x2+y2)

A: