3 ) Express f(t) in terms of the unit step function u(t).

Q: Find the linearization of the function f (x) = x' at x = 1. L (x) =

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Q: Find linearization of the function f(x) = Vx + 3 at a = 1 and use it to approximate V3.98

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Q: f(x) = 'dt th (2) 3=

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Q: y = x – 2 + Ce* X-

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Q: A:- Find the orthogonal trajectories for functions In -1) = - COS X +a y

A: The given family of curves is: lny-1y=-cos x+a ,            where a is an arbitrary constant.

Q: Find the error propagated from the function y = x³ if an error of 0.05 occurs in the independent…

A: For a function y=f(x) If  error in y is ∆y when error in calculating x is ∆x dydx=∆y∆x

Q: Find the linearization of f(x) = 9 – dt at x = 1. 2+t

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Q: Find the linearization L(x)of the function at a .

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Q: secx 1 Given g(x) : z dt , find g'(x). t2

A: gx = ∫7sexcx1t2dt           = ∫7sexcx t-2 dt        = t-2+1-2+7secx      =t-17secx-1 = secx-1-7-1-1…

Q: 3. Find the linearization L(x) of the function at a. F(x) = Vx, a = 4

A: Use the formula for the linearization of a function about any point.

Q: d Use the chain rule to calculate f(x), if f(x) dx, dt. -x12 f(x) =

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Q: Find the linearization of the function given below at the specified point. f(x) 4 In(x) at a = 1…

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Q: 4. Find the general form of the function that satisfies dP/dt = -3P(t).

A: A separable differential equation can be solved by separating the terms in each variable and…

Q: Find the orthogonal trajectories of the functiony x + ce which is passing through (-2,0)

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Q: 1losamlov ç5x3-1 Differentiate the function g(x) = [°*¯'sin t dt. -3

A: We have to differentiate the given function.

Q: Use variation of parameters to find a particular solution of the ODE y" – y = 2e".

A: Given differential equation is  y''-y=2ex we have to find  the particular solution of this…

Q: fCx)=(1+x)* at X=0 is LUX)=1+ KX + "७) %3

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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 linearization of f(x) = 3+ S" sec(t - 1)dt at .2 END x = -1

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find the linearization of the function given below at the specified point. f(x) 2 In(x) at a = 1…

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Q: Find the linearization of the function f(x) = sin(x) at a = π and use it to approximate the number…

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Q: Find the linear approximation of the function y = x at point xo = 1 .3 О а. у%3D Зх - 2 О Б. у3D 3х…

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Q: Find the maximum rate of change of the function f(x,y) =4x^2-2y^3 at the point (1,1)

A: Given data: The given function is f(x,y)=4x2-2y3. The given point is (a, b)=(1, 1). The expression…

Q: (8) Find the linear approximation of the function f(x) = Va at a = 25 and use it to approximate the…

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Q: 4. F(x) = (1- t) dt %3D 4

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Q: (a) Find the linearization of the function f(x) =x+ at x= a=1

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Q: Find the linearization of the function f(x): L(z)= ab a --4x-5 va a न 4x+3 at z=-1 sin (a) E

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Q: Find the linearization of the function f (x) = x° at z = 1.

A: Given, f(x)=x6

Q: 3t – 2 dt t + 1

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Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a =. 3 L(x) =

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Q: Find the equation of orthogonal trajectories of the given function 8x² + y² = c.

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Q: Find the error propagated from the function y = 3x* if an error of 0.04 occurs in the independent…

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Q: 3. If f(x) = [ v19 +r² dt , find f'(3).

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Q: 7 For the function eX, the linear approximation around x = 2 is %3D

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Q: Express x = ln(7t), y = 9-t in the form y = f(x) by eliminating the parameter.

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Q: A function y(t) satisfies th

A: Given, the differential equation                       dydt=-y4-3y3+4y2

Q: Find the linearization of the function f (x) = a° at a = 1.

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Q: Find the linear approximation of f(x) = Vx +I at a = 1.

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Q: Find the linear approximation of f(x) = Vx at xo = 27.

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Q: 2. Determine the critical points of the function: R(y) : y2 – 6y -

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Q: Find the linearization of the function f(x)=x2+2cosx at a=0.

A: Linearization of a function f(x) at x = a is given by, Now,

Q: (b). Examine the behavior of e*+iy as x → -.

A: Euler's formula states that for any real number x  Any complex number z = x + iy,  can be written…

Q: 13. Prove that the function 2x 1 dt t F(x) is a constant on the interval (0, ∞ )

A: The student has specifically asked for the solution to Question-13. Hence, that question is solved…

Q: Determine all the critical points for the function f(t) = Vt² (2t – 1)

A: The given function is ft=t232t-1. Critical points are the points where the function is defined and…

Q: Find the linearization L(x) of the function at a. f(x) = Vx, a = 16

A: