Use the chain rule to find ∂z ∂s and ∂z ∂t . z = tan  u v , u = 4s + 5t, v = 5s − 4t

Q: Use the IVT to prove that the curves y = x2 and y = cos x intersect.

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Q: Find the Integrating factor of: dy + y. sec5x = tan5x dx 1 (sec5x + tan5x) 5 O sec5х — tanп5x + 5 O…

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Q: Use the Chain Rule to find ∂z/∂s and ∂z/∂t. z = tan(u/v), u = 3s + 9t, v = 9s − 3t…

A: The solution is shown in step-2

Q: Use these equations to find ∂z/∂x and ∂z/∂y for the following. x9 + y7 + z3 = 4xyz

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Q: Find tan a. V[ ? (V5, -/7)

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Q: Find the Jacobian for the change of variables defined by x = r cos θ and y = r sin θ.

A: To calculate the Jacobian for the change of variables, we need to calculate the following…

Q: [ 64–x² 64-x²-y 2x? dzdydx. Use cylindrical coordinate to evaluate La LIe4-r2 So

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Q: Find ∂z/∂t if z = sin(5x3-3y2), x = 2s2+t2, y = 2st3. Write in terms of the two independent…

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Q: Let w = iz2-4z+3i. find (a) Δw, (b) dw, (c) Δw-dw at the point z=2i

A: Consider the provided question, (a)

Q: Trace the curve r² = 4cos⁴(theta) tan²(theta)

A: The given curve is r2=4cos4θtan2θ

Q: Differentiate, T. (cb-da-dbT btd with respect to T

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Q: Determine whether the functions y₁ and y₂ are linearly dependent on the interval (0,1). y₁ = tan…

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Q: Evaluate F dr where C is the line segment from (7,-,1) to (20, 1, and F (sin(yz) + 1)i + (zz cos(yz)…

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