11. Determine the solution of the initial-value problem Uu = c²ure, u (x, 0) = f (x), ut (x, 0) = g (x), t > 0, "00 > x > - -0 < x <0. Utt

Q: 6. (1 + x)y' + y = √x

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Q: (1) If f(x) = x¹0, then f'(x) =

A: According to bartleby guide line we do only first part of multiple questions. please re-post other…

Q: · Sº t³ dt then f'(x)= If f(x) = and f'(-2) =

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Q: If U and V are positive constants, find all critical points of F(t) = Ue' + Vet.

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Q: Find the equation of the tangent link to f(x)=x³+x²+x @x=3 A y=34x-63 B D y=-12x-36 y=12x-36…

A: 20) The function is  f(x)=x³+x²+x  Note:- As per the rules, we are supposed to answer the first…

Q: 4 - Let y = f(x) = (a) Find f-'(y). (b) Solve the equations f(x) = a for a = –1,0, 0.5, 2, 3.7, T,…

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Q: y = - 1.5 cos (3x -90) +0.5   what is the    a) period  b) amplitude  c) the phase shift

A: Since you have uploaded multiple part questions according to our guidelines we have solved the first…

Q: A function h(x) = = Compute h'(3) if x-2 f(x) f'(3) = 2 and f(3) = 1. is defined in terms of…

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Q: The derivative of h(y) = (2y² − 3y)˚(y + 6)² requires the product rule and is given by h'(y) = (2y²…

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Q: 6- y = f(x) 5. 4 3. y = g %3D 2)

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Q: This answer is incorrect, could you please attempt it again?

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Q: If f(x) = √² +³ +7 +³+7t2 +3 dt then f'(x) = and f'(x) =

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Q: GivenF(x) = h(f(g(x))), g(1) = 2, g′(1) = 3, f(2) = 4, h'(4) = 1 and f'(2) = 6, findF′(1)

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Q: 6. Find all critical numbers and use the Second Derivative Test to determine all local extrema. a)…

A: for part a see 2nd step. for part b see 3rd step.

Q: 6. Using the Second Derivative Test, what can be concluded about the positive critical value…

A: Given query is to find the correct option for postive critical value.

Q: A particle moves along the x-axis so that at any time t > 0, its acceleration is given by a(t)=…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 6. If f(x)=3x' -+ 4 + 4x +1, find f(x) and f"(x).

A: Given query is to find the Indicated derivative.

Q: (t²,0 2 7. in terms of unit step function, hence obtain LT. %3D

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Q: Siven that y = f(x) passes through (2, 1) and f'(x) = 3x² - 5x, find f(x). %3D

A: Given query is to find the function

Q: 1) If h(a) = a + 1, find h-(x). (A) h-(x) = 3+ (x+ 2)3 (B) h-(x) = V – I (C) h-(x) = 2a3 – 3 %3D %3D…

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Q: Q3/ Find f'(x) = y' 1. y = (2vx-4)5 2. y = (x+2)2 3. f(x) = x43 2 ++3

A: Use the power law of derivative and chain rule of derivative.

Q: Q1 Suppose g(2) = 3 and g'(2) = = -2. then find the following. 1) If f(x) = (x² + 3)g(x) + g(2) find…

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Q: If y" = 1 (x + 1)² y(0)=2 y'(0) = 1 then y'= and y=

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Q: 1. Find the third order derivative f"(2) of f(x) = x³. Of" (2) = 1 Of" (2) = 0 Of" (2) = 12 Of"" (2)…

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Q: 8. The velocity of a particle moving along a straight line at time t is given by v(t) = 2t – 2t3/2 –…

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Q: Find f"(x) if f(x) = = 25 x-4 70 (x − 4)²

A: We need to calculate f''(x) for the given function f(x). This can be evaluated as follows: