Find exactly T (t) and N(t) for x = [Choose the correct answer.] T (0) = T (0) T (0) T (0) = = = (i −j+k) and N(0) (i − j+k) and N(0) (i+j+k) and N(0) (i+j+k) and N (0) = = = = e¹ cost, y = e¹ sint, z = e¹ for t = 0. (-i-j) √/₂2 (i+j) √/2(-i+j) √(1-j)

Q: Ury is 10. (i) Show the general solution of the PDE u(x, y) = F(x) + G(y) for arbitrary functions F,…

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Q: Show that (a) x(t) * 8(t) = x(t)

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Q: Is the two functions h(t) and g(t), is h-1g-1 (t) = (hg)-1(t)

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Q: Let X b(n,-) and E(x) = E(2– 6x) find n.

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Q: Find y as a function of x if x²y" +5xy - 12y = x², y(1) = −9, y(1) = 9. y=

A: We have to find as a function of .

Q: 11. In the function y = 3x2 - 3, y is replaced by y and then y is replaced with y +2 ; the new…

A: Given:     Function y=3x2-3   Here y is replaced by 12y       substitute y=12y      12y=3x2-3…

Q: 3. Find f(x) and f (x) if f(x) = lnx + 2cos³ x. %3D

A: First use sum/difference rule of differentiation f±g=f'±g' then use the following formulae: dln…

Q: Let h(x)=f(g(x)). If f(−4)=−3, f′(−4)=−1, g(1)=−4, and g′(1)=3, find h′(1).

A: The formula one have to use here is f(g(x))'=f'(g(x))* g'(x)

Q: If f(x)=3x-²-5x¯³+1 and g(x)=√√x, then derivative of (gof)(x) is: a. b. C. 1/1/23 1 2 3x ² 5x 3 1 d.…

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Q: 3 - 9, y(0) 33 - 30 – 13 a(t) = y(t) = %3D

A: Given,       x'y'=53-30-13xy     x(0)=-9, y(0)=33

Q: Compare the values of Ay and dy if f(x) = x³ + x². 2x + 1 - æ is changes from 2 to 2.05.

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Q: If f(x) = 2 + 3x – 4x², determine the value of the dependent variable f(5) – f(3). Show your work.

A: We can solve the problem by putting the value 5 and 3 in the given function.

Q: Linearize f(x)=√√√2-x for a = 1 and use it to approximate the value of √1.6. L(x) =

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Q: If f = {(0, 1),(1, 2)}, (b) find h(x) = f(5 − 3x) − 2.

A: From the given data f(0)=1 and f(1)=2 That is f(x)=x+1