x+6 lim 2. X6 X -36

Q: B. For each of the following functions z, find and dx²' dyðx' axðy' dy2 1. z = 2x² – 5xy + y²

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A: As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And ddxtanx=sec2xddxex=ex…

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A: This question is based on vector projection.

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Q: Step 2: Step 3: Sten 4:

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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

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A: Here, to find the valid trigonometric substitution.

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A:

Q: y =1+6.x% Osrsl for Find the exact length of the curve

A: Length of the curve

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A:

Q: (ii) Prove the identity (2 - 2 cos 0) (sin 0 + sin 20 + sin 30) -(cos 40 - 1) sin 0 + sin 40 (cos 0…

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A: We will use sigma notation.

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A: This question is based on application of integration.

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Q: Evaluate each limit: x +x-30 a) lim x-3 x-6x+5 3-1-4x b) lim X-2 x+2 x+3 c) lim x→-3 Vx-5+2

A: Limit

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A: Given: Now find the point of intersection between the curve y=x2+2 and the line x=2. y=x2+2 ;…

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

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A: Explanation of the answer is as follows

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A: Given problem:-

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Q: Evaluate the integral [(4?) i + (3) j+ (5t + 3) k] dt. 1 i + (3) j+ (5t + 3) k] dt = (O i+ O ij+ (O.…

A: Topic = Integration

Q: Solve

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A: To find out the characteristic equation.

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).

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A: