Find the unit tangent vector T(t). r(t) = t2i + tj +4k , P(9, 3, 4) T(3) = Find a set of parametric equations for the line tangent to the space curve at point P. (Enter your answers as a comma-separated list. Use t for the variable of parameterization.)

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Q: 5. Find the general solution: 9y" + 12y' + 4y = 0.

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Q: Consider f(x) = (5x + 11)2022, find: i. f'(x) ii. f"(x) iii. f''(x)

A: Given Data: f(x)=5x+112022 Formula used: dax+bndx=nax+bn-1dax+bdx dxndx=nxn-1

Q: Find div F and curl F if F(x,y, z) = x2°i+ 4y°x²j+ 2z²yk. div F=|2° + 12 y? x² + 4 z y curl F= 2 z2…

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Q: 14. Evaluate L{e" cos(30)}. s-4 A) s - 8s +25 B) s - 8s + 25 4 C) s - 8s + 25 s+4 D) s - 8s +25

A: As we know that the Laplace identity; 1). If Lft=Fs then Leatft=Fs-a  2). Lcosat=ss2+a2   Given:…

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A: Given : f(x)=7x+1   To Find : a) Derivative of f(x) b) Tangent at point (a,f(a)) where a=5

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A: Solving

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A: Here, x=t3y=9-t

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Q: 23 + 7x + 9 Find dy: y = 1² + 4 dy :

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Q: dy Solve the separable differential equation dt t t?y + y Use the following initial condition: y(0)…

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A: We will start from critical points and follow upto inflection point

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A: We can solve this as follows:

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Q: Consider f(x) = (5x + 11)2022, find: i. f'(x) ii. f"(x) iii. f''(x) iv. fiv (x) v. f°(x)

A: Given, f(x)=5x+112022

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Q: Let A = 2. Find the eigenvalues of A 3.

A: Use eigen value concept