f(t) = 19(0.987)'; f(t) = Qoe -kt

Q: dz Use an appropriate form of the chain rule to find dt z = 9x10y%; x = t10, y = t6 Enter the answer…

A:

Q: If f(z)=u(x,y)+iv(x,y), how do I determine dz? I have that the answer is dz=dx+idy, but I don't…

A: It's nothing to do with f(z)=u(x,y)+iv(x,y). Here z be complex independent variable. Hence , z could…

Q: Find the linear approximation at x = 0 to Write your answer in the form y = Ax + BỊ.

A:

Q: Solve for F(s): 01

A: Given function is ft=0,      0<t<1t,        t>1             ...(1) To find: Laplace…

Q: Find the antiderivative F(x) that satisfies the given condition. dF dx = 4e* + 4x²; F(0) = -5

A: Given query is to solve the differential equation.

Q: dy Let y = (x2 – vx)4". Find using any method. dx -

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Q: dy from t dx n for y as a function of x, and find two results are consistent by expressing the (a)…

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Q: dx Q2 / Use the chain rule to find ( ) in terms of x and y dy y = ( 2 1 1, at t2 t = 2 and X t + 1.

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Q: Find F(s). F(s) = £{t¹8e-4tz X

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Q: Given y = V4x + 5, find the differential dy when a = 7 and dæ = 0.3. %3| Round your answer to three…

A: Given data:   The expression for the given function is y=(4x+5)1/2. The given value of x is x=7. The…

Q: dy dt t2

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Q: Solve the initial-value problem for a as a function of t . dx (t² – 6t + 5). = 1, (t > 5, x(8) = 0)…

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Q: Q4. If y= f (t) and x=f (t) d²y dx2 dy 3 and %D 4t dx2 dy By using chain rule, find dt

A: Chain rule is given by dy/dx=( dy/dt )× (dt/dx)

Q: F (s) 1 = s(s²+2s+5)

A:

Q: dz Use an appropriate form of the chain rule to find dt z = 8x"y³; x = t°, y = t Enter the answer in…

A: Topic :- Differentiation

Q: dy/dt= 2e-t/8, t is greater than or equal to 0

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Q: If y = t“, then dy 4t³. dt

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Q: Find dy if x=t+6f and y= dx 2 5 at t=1 +

A: We have to find dy/dx

Q: Solve the initial value problem for y as a function of x. (x² + 25) dy %3D 29, у(5) %3D 0 dx

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Q: Verify the final value theorem of f(t) =1+et[sint + cost]. O- 1 1

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Q: Find the linear approximation at x = 0 to Write your answer in the form y = Ax + B.

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Q: dy Solve the initial-value problem for y as a function of x. (49 – x²). dx = 1, y(0) = 4 Y =

A: We will solve this integration using trigonometric substitution as follows

Q: Find f(t). s(s + 1).

A: L-1[F(s−a)]=eatf(t) From first shifting property, L{e^(at)*F(t)} = f(s-a)…

Q: For f(x, y) = 2y3 + x² – 4x – 4xy – 9, find the critical points and use the - Second derivative test…

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Q: Find the total differential z = 1/2 (ex2+y2− e−x2−y2)

A: The given function is z=12ex2+y2-e-x2-y2. Note that  ∂z∂x=12ex2+y22x-e-x2-y2-2x=xex2+y2-e-x2-y2…

Q: 크(F(a+) e dt dx 19

A: We have to evaluate, ddxFx4=ddx∫10x4  e-t2 dt

Q: If f(x)dx = 32, then f(t)dt : %3|

A: Here, Order of limit has been exchanged with each other.

Q: wherey = x + C is a solution to this DE. What is the particular solution?

A: Let's find.

Q: t²e*dt dz J2r

A: on solving this we get the

Q: dz Find dt(t=1,s=0) when z = 2x3 + 15y3, where x = t2 - s and y =t+ 2s2

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Q: Find the G.S.of the DE. (ytu dy=D0

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Q: 2. Find dy where y = v3x3 +4x + 1.

A: Given y=3x3+4x+1

Q: d Use the chain rule to calculate f(x) if f(x) In (1+ tº) dt. dx, 0. f(x) =

A: let's use chain rule and find derivative of integral.

Q: Find the gradient ∇f of the function f given the differential. df=2ye^xdx+xe^xdy   ∇f=

A: Note that            . Here, df=2yexdx+xexdy. So, here we have fx(x, y) = 2yex and fy(x, y) = xex.

Q: Find the total differential. z = 10x4y5 dz = (No Response)

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Q: B) Find Sx e2x dx, at h = 0.2, use Simpson's 1/3 rule. J0.4

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Q: 2. Solve the IVP 2x + y + 2xyy' = 0, with y(1) = –2. d (Hint: This ODE is neither first order…

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Q: 51. grad f = (2x + 3e")7 +3xe'j

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Q: dy Solve the initial – value problem: = y² given that f(0) = -1 dx %3D

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Q: Solve the initial-value problem for a as a function of t . dx (t2 – 11t + 24) = 1, (t > 8, x(9) = 0)…

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Q: Find the linear approximation of y = V1+ x at x = 0 and use it to approximate V1.05 7.

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Q: dw Q11- express by using the chain rule: dt w = ln(x² + y² + z²) x = cost, y = sint, z = 4√t

A: We have to express dwdtby using the chain rule:

Q: dy Find dt y = 3t(21 – 5) $ II 히

A: The product rule of differentiation states that ddx[f(x)g(x)]=g(x)ddxf(x)+f(x)ddxg(x) The chain rule…

Q: [" In(y+z) e dxdzdy = [Show your solution.]

A: Given that,

Q: g(x) f(x) - sin(2²) dt, find f(x). = J

A: To Find: f'(x)

Q: Solve the linear ODE using an Integrating Factor. dy dx - 3y = 8e5x

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Q: Find the G.S. about xo = 0 for: (x² + 4)y" + xy = x + 2

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Q: Use the Quotient Rule to compute the following: t2 + 1 at t = -2 dt \ t2

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Q: (b) If z = 9t²e 4t, find 4 dz dt

A: Given.