If z =e* + In(xy) Evaluate- ,and ,at the point (1, 2). Hence, calculate the change in z when x changes to 0.8, while y does not change.

Q: f(x) = acos(b\x) x2 COS

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Q: 2) Compute the approximate derivatives of In x I+ x2 fCx) at x-2, using three- endpoint formula…

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Q: Compute the following derivatives using the chain rule. g(y) = ln(1 + y).

A: Take 1+y = t  And use chain rule

Q: Use linear approximation or differentials to estimate the following

A: Solution: Consider the given number: 1000.033 Let y = x3 = x13 Differentiating with respect to x:…

Q: (b) To determine To compute: The differential equaiton + x = sin 4t with initial condition x (1₁) =…

A: Given differential equation is: d2xdt2+x=sin4t . . . (1)The initial condition is: xt1=0 And…

Q: Calculate differential: f (x) = = e-* cos(3x) + 2 of the range [1,2] with h=0.05 a) Using the…

A: Equation is f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of the…

Q: Assume mmh (x) = f(g(x)) such that the first an exist g Second derivatives of both of and What is b"…

A: Assume h(x) = f(g(x)) such that the first and second derivatives of both f and g exist  We have to…

Q: |- find the general Solestion of the differential eq ladich

A: Note : According to company guidelines we can solve only first question. So please post other…

Q: A 20 kg wagon moving at a speed of 0.5 m/s towards right collides with a 35 kg wagon which is at…

A: Solution:

Q: Use Milne's method to obtain the value of y(0-3).

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Q: Find the derivative of f (x) = Ln e*+1 using the limit process. %3D

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Q: use differentials to approximate the change in y if x changes from 25 to 25.3

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Q: Approximate the length of the curve using n secant lines for n = 2; n = 4.y=ln x, 1>=x>=3

A: We have been given a curve y=lnx and we are supposed to approximate the length of this curve between…

Q: of the differential equati

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Q: Verify that the derivative and integral results for a general base b reduce to the expected results…

A: Note that ddxbux=lnbeuxu'x,∫bxdx=bxlnb+C.

Q: |х — 1 x5

A: Use the method of substitution to evaluate the integral. I=∫x−1x5dx=∫x−1x52dxLet u=xdu=12xdxSo,…

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y= In(In 9x)

A: The solution for the above question is as shown below.

Q: Use a linear approximation (or differentials) to estimate the given number. (1.999)3

A: First I have find the linearization of x^3 near x=2 and then find the required approximated value.…

Q: (3) Compute the derivative of the function e2t cos tdt.

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Q: Suppose that 3 of work is needed to stretch a spring from its natural length of 30 cm to a length of…

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Q: Prove that E = ehd.

A: By the defination, fx=fx+h....1∆fx=fx+h-fx∆fx=Efx-fx∆fx=E-1fx Therefore, ∆=E-1E=1+∆.....2

Q: . Compute the central difference approximations of O (h^4) for the first derivative of y = cos(x) +…

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Q: Use a linear approximation (or differentials) to estimate the given number. (1.999)5

A: Given term is (1.999)5Let x = 1.999

Q: find the derivative of y with respect to x, t, orθ, as appropriate.

A: On simplification, we get

Q: Use differentials to approximate the value of <2.1.

A: Given  Find the value of 52.1

Q: complete solution

A:

Q: If X; derive the moment-generating function (mgf) of X?. Ν (μ, σ) :

A: Given X~ N(mu, sigma^2) We want to find the mgf of X^2

Q: What is the derivative of y = e3 In(5 + e3)? %3D

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Q: Use linear approximation (or differentials) to estimate the given number. 3 а. V8.12

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

Q: A particle is moving with S. H. M. while making an excursion from one point of rest to another, its…

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Q: Suppose f is differential equation on (-inf, +inf), f(3)=12 and f'(3)=-2 use linear approximation to…

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Q: 5) Form a DE by eliminating the arbitrary constants from the equation y = asin(4x + 1).

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Q: Suppose that a drug is administered to a person in a single dose, and assume that the drug does not…

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Q: If u, v, w are nonzero differentiable functions, then the first derivative of uv / w is

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Q: 24. What does it mean to say that dV is an exact differential?

A: What do you mean by dV is an exact differential.

Q: Solve the nonhomogeneous ODE by variation of parameters. ODE: y" + 4y = cosh 2x

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Q: what is the differential coefficient of x.

A: To find differential coefficient of x we need to differentiate x with respect to x.

Q: Use a linear approximation (or differentials) to  estimate the given number.  (1.999)4

A: Consider  1.9994

Q: (a) Find the first derivative of the function y= la) with respect to x by using the chain rule.

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Q: Apply the first order forward difference formula to find the derivative at x = 2.1. fx) 1.2 0.694444…

A: We need to find the derivative of the function f(x) at x=2.1 by applying first order forward…

Q: Evaluate the 3rd derivative of M with respect to (x) M= x6 y3 Cos (x6 y3) if x =6 and y= 3

A: The function is M=x6y3cosx6y3. Using implicit differentiation, find dydx.…

Q: 5. Compute the derivative, r'(t), of r(t) = (et-4, t, In(1 – t)).

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Q: Use a linear approximation (or differentials) to estimate the given number. e−0.01

A: Let f(x) = ex, where x = –0.01. Then f(0) = 1.

Q: Compute the derivative of y = In ( VI-2 conh z - (z² + 2) -(2- 1)

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Q: 2 e -8; x(0) = 1 dt

A: Solution is given below:

Q: Let f(x, y,z) = z-sin(xy), x = t, y = In t, z = e4. Find derivative of f directly and by using chain…

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Q: 4. Find the Linearization of f (x) sinx at a Provide your answer as L(x) =?

A: The given problem is to find the linearization of the given function at given point. Given…

Q: (In iny

A: To find the derivative of the given function- lny=lnxylny Here we will use the following formulas-…

Q: Compute the following. (a) limz-2i (2z+3)(z-1) z2 – 2z+4 (b) Derivative of (1 – 22)*. - IT/4 (c) S7…

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