2. Find the volume of the solid bounded by z = 0, x = y2,z= 3, x = 4 - y2. (graph the solid)

Q: 2. Suppose z is a function of a and y and tan(V+ y) = e*. Determine dz dz and 2

A: Suppose z is a function of x and y  tan (√(x + y)) = ez^2  We have determine ∂z/∂x and ∂z/∂y

Q: he Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 5+x2 Ciuo Hooim

A: Here we have to use linear approximation rule.

Q: Give the symmetric equations of the line l perpendicular to the plane T : 5x – 2y = z+4 and passing…

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Q: Evaluate sin (44º) + cos (29º) using differentials. Refer to special triangles.

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Q: 4s + 12 s2 + 8s + 10 4e -4t – 4te -4t 4e4 + 4te4t Option 3 Option 2 -4t 4e + 4te¬4t

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Q: 2y(x? — у + х)dx — (x2 — 2у) dy %3D 0

A: I think mistake in question inplace of -ve sign.

Q: If a > 0 and [[ 20*+v 20+u° dr dy = 1(e* – 1) , a =?

A: Using polar coordinate evaluate the above integral

Q: Let N1 (h) be the approximation of f'(xo) with some numerical differentiation scheme depending on h.…

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Q: 5x - 4 and the a-axis over the interval 6 Find the net signed area between the graph of the function…

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Q: What is the farthest point on the sphere x2 + y2 + z2 = 16 from the point (2

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Q: (D³ - 3D² - D + 3)y = 0

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Q: Find f5(x) if f(x)= 3√3x+2

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Q: 3. f(x) = (2x + 1)3 4. f(x) = V7 + V3x + 1

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Q: Find all horizontal and vertical asymptotes (if any). (If an answer does not exist, enter DNE.) 10x3…

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Q: In Exercises 9 and 10, find all the trigonometric values of 0 with the given conditions. 15 9. cos 0…

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Q: Question 1 Compute v31.6 approximately by use of differentials. O 1.995 O (E) None of the choices O…

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Q: 3) lim-) 1 х-1 \x-1 In x)

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Q: 1 е. (s²+1)(s²+4s+8)

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Q: Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05 cm thick to a…

A: Given problem:- Use differentials to estimate the amount of paint needed to apply a coat of paint…

Q: VII. Use Lagrange Multipliers to solve the following: Maximize f(x, Y, z) = 4x + 2y + z %3D subject…

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Q: Determine a.5 tor each of the following i = (7, -3.5)andb = (-5,11. -2) b) a = (-15.13), 5 = (14,…

A: If a→ = a1 , a2 , … , an and b→ = b1 , b2 , … , bn then  a→·b→ = a1b1 + a2b2 + … + anbn

Q: 2. Evaluate the integral / 2 (a³ + 3)/4 dx. 4 4 (a) 5(23 + 3)/4 + ( +3)5/4 + C 27 27 (b) 푸(고+3)%4…

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Q: For the function f (x) = x4 - 4x3 + 5, find the local and absolute extrema and any points of…

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Q: Find the minimum and maximum values of the function y = 8Vx? +1 – 5x on the interval [0, 3] by…

A: To find the minimum and maximum values of the function y=8x2+1-5x on the interval 0, 3 by comparing…

Q: 2) lim- x) Tanx

A: The given limit is              limx→π2π2-xTanx we know,     Tanx= sinxcosx

Q: lo-2 2 (12y-8x) dy da

A: Given: ∫05∫0z2∫010-2z12y-8xdydxdz

Q: A particle is moving along a horizontal path which starts at a distance of 5 ft to the right of a…

A: We need to determine if the particles collide or not.

Q: Consider the function g defined by g(x, y) = sin (T /Ty) + log3 (x – 3y) Do as indicated. 1.…

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Q: Find two positive numbers whose product is 2 such that the sum of one number and the square of the…

A: Suppose, we take ?as a negative number having absolute value. Take a pair with the value much more…

Q: Use the method of Lagrange multipliers to maximize the function f(x,y,z)=4x+2y+z subject to the…

A: Let's find.

Q: Find, the genetal Solution o the differehtial equation (2x+Y-3) dy= +2Y-3)dXf %3D

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Q: 1 0 0 0 0 1 2 -6 2 -8 10 1 0 1 0 3 -2 -5 -16 |

A: We have to multiply: 1000012-60010003-22-8-5-16

Q: Use Method of Variation of Parameters: [D² - 8D + 16]y = e4Xsec2x

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Q: dx 5x2 + 16

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Q: 4. 25t 1 dt

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Q: The edge of a cube was found to be 20 cm with a possible error in measurement of 0.2 cm. Use…

A: As we know that; The expression for the volume of the cube is: V=a3    ....(1) Where a is the edge…

Q: 1- x² tx

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Q: Find the particular solution to the differential equation d²y = 4e* + 3x² given y = -3 dx2 and = 3…

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Q: (ost) X= 3サ-3 DiD X-2-2y ¥ーにh で3,0) D3 Dy メーと2 サ=スメート X-4 <-リ-3 toノー4)

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Q: Question 1 Determine the inverrse Laplace transforms of: 2s2-5s-1 (a) (s+3)(s²+9)

A: L-11s-a =eat L-1as2+a2=sin(at) and L-1ss2+a2= cos(at).

Q: lim Vxe 2

A: Given query is to find limit of the expression.

Q: y" + y= tanx

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Q: Suppose z is a function of x and y, and tan Vy? +x² = ze6y. Solve for and dx ду

A: Here, given that z is a function of x and y and tan y2+x2=zxe6y⇒tan y2+x2=ex ln ze6y...(1)

Q: c) y(x) = c, + cz + Acos3x + Bsin3x Q.6) The singular point (s) of (x² + 4)y" – x y' + 4y = 0 , is…

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Q: 1 (s+1)(s2 +1) + cos t - sin t) + cos t – sin t) O Option 4 O Option 2 5(e-cost + sin t) 5(-e+cos t…

A: L-1{ 1/(s2 +1)(s+1)} expand it  L-1 {-s/2(s2+1) + 1/2(s2 +1) + 1/2(s+1)} L-1 s/(s2+1) = cos(t) L-1…

Q: SIn(5 + VT)dr Algebraic Substitution

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Q: 4. Evaluate the integral 2+ In? x -dx. x – x ln x (a) 3 ln |In a – 1| + 2(ln r – 1) + (In a – 1)2 +…

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Q: Question 3 (a) Find the first and second derivative of the following function, in which a and b are…

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Q: _4. What is the area of the enclosed regions in problem number 3? A. 10 sq. units B. 12 sq. units C.…

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Q: dx Vx-4x-7 S- -dy y2-8y+5

A: The given integrals are' 1)1/sqrt(x2-4x-7)  2)7/(y2-8y+5).