if x<1 4x2 Is the function g(x)=: 2x differentiable at x=1? if x>1 O No, since g(x) is undefined at x=1. O Yes, and g'(1)=3. O Yes, and g'(1)=8. O No, since g(x) is discontinuous at x=1.

Q: If the change of variables u=x²+4 is used to evaluate the definite integral f(x) dx, what are the…

A:

Q: Find a function f € span(1, cos x, sin x) which minimizes the integral 2πT √²* |x +1 − f(x)| ²dx.

A: Given a function                     f∈span1, cosx, sinx

Q: That the value of the integration g(1) = 00 , g(2) = 0 1-e t) -dt 9(t) where g is a function that is…

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Q: Use Taylor’s formula with a = 0 and n = 3 to find the standard cubic approximation of ƒ(x) = 1/(1 -…

A: The given function is,

Q: Given f(x) = 8x3 + In(x – 1). Estimate the value of f(2.01) using differential. %3D

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Q: That the value of the integration g(1) = 0, g(2) = 0 1-e) -dt where g is a function that is…

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Q: hi, i've added the problem as a picture please take a look. thanks in advance!

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Q: According to numerical methods, the integral of a function f(x) over the limits a and b can be…

A: Given data  Used Simpsons 1/3 rule  f(x)=7e^(-πx)(sin(x^2)) With a=0 and b=2 and number of intervals…

Q: 1.x3 = at?, find the second derivative of "x" with ,d²x respect to "t", 'dt2

A:

Q: 1. If z = 2xy – 3x²y and x is increasing at 2 cm/sec determine at what rate y must be changing in…

A: Z is neither increasing nor decreasing at the given instant. A function is said to be neither…

Q: evaluated at x = 0.001 and y = 0.002 Compute the derivative of the following: 5 g(x) =, 2.1'x f(x) =…

A: topic - derivative of a function

Q: 1 (5* )csch dy if Find dx 1. (а) y x>0. (ecosh 5x ) In Vx +1 d Show that for x 2 1, coshx- dx (cosh²…

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Q: 5. If the function y = y(x) is such that dy + 2y = x cos r, dr use the integrating-factor method to…

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Q: find the absolute extrema of thefunction on the closed interval. y=x^{2}-8 \ln x,[1,5]

A: Given:- function y=x2-8 Inxdefined on the interval 1, 5 The derivative of the function is y'=2x-8x…

Q: Find the linear approximation of f(x) = lnx at x = 1 and use it to estimate ln(1.02). L(x) =…

A: Given that: f(x)=lnx

Q: Differentiate the following functions in derivative and differential forms: f,(x) = Ax f,(x) = In x…

A: For f1(x)=Ax ⇒f'1(x)=Adxdx⇒f'1(x)=A Sketch of f1(x)=Ax limx→∞A=A

Q: Verify directly from (3) that the solution has derivatives of all orders in {z > 0}. Asume that h(x,…

A: Sol

Q: Find the linear approximation of f(x) = ln x at a = 1 and use it to estimate In(1.2). L(x) = In(1.2)…

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Q: Note that the solution of the DE: y(x) = e* (S e*~*dx +C) contains an anti derivative which has no…

A: Note: As there is not any point as d. So we cannot solve question h.. Here is the solution of f…

Q: Suppose x4 e−4y = ln (xy).Find dy/dx by implicit differentiation.

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Q: Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate In(1.18). L(x) =…

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Q: fy = f(r), how do we define the differential dy

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Q: From the differential equati on by eliminating the arbitrary function ffrom xyz = f (x?+y'+z°).

A:

Q: If f(x,y) = y2 ex + 3 ln (xy), find fxyy (1,1). fxyy (1,1) = ?

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Q: 9. Find dy/dx by implicit differentiation of y? = In(x), at (e36,6).

A:

Q: 1.) Find the equation of the line tangent to f(x) = 6 ln(7– 3x)+5e-4 – 6x – 2 at x = 2 2.) Find the…

A: According to the guidelines issued by the company We are supposed to answer only one question.…

Q: Find the differential dz of the function f(x,y)=4y2+x2y−2xy and use it to approximate Δz at point…

A: Find the differential dz of the function f(x,y)=4y2+x2y−2xy and use it to approximate Δz at point…

Q: A 1125 m³ open-top rectangular tank with a square base x m on a side and y m deep is to be built…

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Q: Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate ln(1.34). L(x) =…

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Q: 60. Is there a value of b that will make Sx + b, x<0 (cos x, x20 continuous at x= 0? Differentiable…

A: A function is continuous at x=c, if LHL at c=f(c)=RHL at climx→c-f(x)=f(c)=limx→c+f(x) A function is…

Q: Let h (x) = x sin . 1. Find the x-values where h has horizontal tangent lines in the interval 0, 27.…

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Q: (b) Use the total differential dz to approximate Az. dz = X

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Q: Q2) A: Compute at the point (1, 0) for the function dx S(x,y) = cot 1(4x + em(sin2xy)) + sinh(3) +…

A: Given that, f(x,y)=cot-14x+elnsin 2xy+sin h(3)+log2x2 Which can be re - written as,…

Q: Find the temperature u(x, t) in a rod of length L, if the initial temperature is f(x) = 100 sin 6Tx…

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Q: 2. Suppose that h(x) is a continuous function, h(-1/4) = 1/2, h(7/4) = 1 and h(2)dx = 2. Evaluate…

A: Here, given that h-π4=12, hπ4=1 &amp; ∫-11h(x)dx=2...(1)

Q: Eliminate the arbitrary constants x = -ln t , y = at + bt^2

A: given  x=-ln t , y=at+bt2 claim- to eliminate the arbitrary constants

Q: 7 If the change of variables u = x-1 is used to evaluate the definite integral f(x) dx, what are the…

A: This question can be solved using the concept of change of limits in definite integrals.

Q: 1) Find dy for each OF Following functions du a) y = cosh (2n) + 4 ny cosh (1an 2) + 2y = e * %3D F)…

A: Product rule of differentiation:   Chain rule of differentiation:

Q: The equation of the tangent line to the graph of f(x)=ln(x) at x=e^−1 is given by y=mx+b for m =…

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Q: Find the particular antiderivative of the function f(x) = e"(2" – 1) whose graph passes through the…

A: Integration

Q: 1. Find for differentiate each of the following functions. dy хр a) (In(coshx) sinh x) g) y = - b) y…

A: Given: a)lncoshx3c)y+4coshx2=exsin-1(2x)g)y=sinhxex

Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x+1) 3- xy + x²y 3 at x = 1

A: Here, We need to find the derivative of the given functions. To solve these questions, we need chain…

Q: . Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0. f (x) has a root in [0]. If we…

A: Newton-Raphson iteration scheme is given by  xn+1=xn-f(xn)f'(xn) We use this formula to estimate…

Q: y is a function of  x and the slope of the function is zero at x=10 then to determine that y reaches…

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Q: Q4: To evaluate the integral fcos' xdx using the reduction formula of cosinc function

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Q: 7. Given y = sinh(e* +tan (2x)-cos (x+1). Consider | dy (i) et 1 dx 1+e2x 1+4x 1-(x+1) dy (ii) ex 1…

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you…

Q: 1. Defermine the integrating thators of the pallo wing non- exnet exact esuations. A. (1+ 4xy -…

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Q: 6 The coefficient of sin( 2r) in the antiderivative of F(x): F(x) = (cos( is

A: We have to find the coefficient of sin 2x.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.