Let m & n be constants and suppose f(x) = {" + 3bx + 2x² , x<1 x > 1' тx + b What are the values of m and n so that f'(1) exists.

Q: f(x, y) = ln (2x) In (3y) + x - y - xy - 3, then fyz (2,-) is equal to

A: Given :fx,y=ln2xln3y+x-y-xy-3

Q: 2. Find the root of f (x) = 2* + x³ – x = 0 by using Newton Raphson method with initial value po=…

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Q: Q2 find the derivative of the following: 1) y = 2stn²(5x) ,2) y = Inx'n cosh 5x ,3) xsin¬14y = y…

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Q: Consider the differential equation, x' = f(x), vith f(x) = { 1 - x x > Compute the solution to the…

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A: f(x)=14+x

Q: From the differential equation by elimanating he arbitary function f from xyz=f(x2+y2+z2)

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Q: What is the first derivative of q(x) = In (4x² + 3x+2)? Select the correct answer below: In (8z + 3)…

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Q: 'the line tangent to the graph of y= In(3x) + 2x e at x=1 6 Jx-1 by using quotient rule. Vx +1 for…

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Q: If N(x) = sin x – sin θ and D(x) = x – θ, find the limit of N(x)/D(x) as x approaches θ. (SOLVE BY…

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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: Find the fourth derivative of f (z) = 37 + In(z) – 164z. Enclose arguments of functions in…

A: To Determine: find the fourth derivative of the function .  Given: we have a function…

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: 2. Find the root of f(x) = 2* +x³ – x = 0 by using Newton Raphson method with initial value po= -1,5…

A: Consider the provided question, fx=2x+x3-xWith initial value p0=-1.5  and…

Q: Q.2 Find the derivative at each critical point and determine the local extreme value. (a) y=x√√4x² 1…

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Q: Suppose X1, ..., Xn are iid with PDF f (x | 0) = 40ªx-5. x > 0, where 0 > 0. Find the method of…

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Q: If f(x, y) = ln(x + y), then total derivative or total differential of f at x = 3 and y = 20 is : Y

A: Given data: The given expression for the function is f(x,y)=ln(x+y). The given value of x is x=3.…

Q: 2- Find the third derivative for əx3 for f(x,y) = sin) )+2 sin) sin)+3cos°) 8y3sinz s()+2sin()…

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Q: Determine the first derivative of the ff. function a. y = 400(2)**3 sin 3x b. y = Vxe2* cos x…

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Q: 9 Derivative of fi») 1x 4 . 5. 1 f) 1x1cosx, fird f'n)

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Q: The differential equation ry" + 3y - 7y=seca is normal on any open interval not containing a = 0.…

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Q: Obtain the differential equation of the family of straight line with the algebraic sum of the…

A: The differential equation of the family of straight line with the algebraic sum of the intercept…

Q: Usually in a method of solution for Homogeneous DE, after the substitution of y = vx (or x = vy) and…

A: In the method of solution for homogeneous differential equation, The equation is of the form,…

Q: Given that f(x, y) = (y + 1) approximate the change in f(x, y) from the point (4, 1) to point (4.03.…

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Q: Use forward, backward and central difference approximations to estimate the first derivative of:…

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Q: Find the differential of w = ln /x² + 3y² + 2z²

A: Here we use chain rule of differentiation to find the required differential. According to chain rule…

Q: 2.Evaluate the total derivative of u with respect to x for u = 6x²+4y² + 4z² when y = cosx and z =…

A: We have to find total derivative of u with respect to 'x'    where     u = 6 x2 + 4 y2 + 4 z2  Given…

Q: The differential equation corresponding to the family of curves y = Asin2x+ B cos 2x , where A and B…

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Q: Jesaki Inc will sell N units of product after spending $x thousand in advertising, as given by  N=…

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Q: 7. Find the differential dy of the function y = x (1-cos(x)). If the error in x is ", find the error…

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Q: Find the differential of the given functions. 1. y= x-2x² + 5 5. у 3 1- -s2

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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: 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: 3. Verify the statement by showing that the derivative of the right side is equal to the integrand…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: * find the dicredional derivative af the. f omc tion and in the direction of a= [o,3, 37 + find the…

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Q: The derivative of y= sech1(Inx)+esinh(3x) equals Select one: 1 3e sinh"(3x) O y' = - xInx/1-Inx…

A: Proceed as shown below...

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

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

Q: B) Find the derivative of the foiiowing: 1) y = 2sin2(5x) ,2) y = x, 3) xsin-14y = y tan-14x 4) y =…

A: As per the company  guidelines we have to solv first 3 subparts if suborats are not mentioned  So…

Q: 17. Show that V10x + 1 and Vx + 1 grow at the same rate_ as x→o by showing that they both grow at…

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Q: If the first derivative of y is -3.8025 sin(0.507 t) on the interval {0 <= t <= 24}, what are the…

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Q: The derivative of y=esinh/x + coshVx equals Select one: 1 1 (esinh/cosh/x + Vx² -1 2х 1 O y' = e…

A: We have to solve

Q: a. Obtain the differential equation of the family of straight line with the algebraic sum of the…

A: Write general equation first of given conditions.

Q: 15 - What is the approximate derivative of f(x) = 5x³ + 4x² if we use f(ze+h)–f(za) forward…

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Q: 13. Obtain the differential equation of the family of straight lines at a fixed distance p from

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Q: A flexible stretched string is constrained to move with zero slope at one end x=0, while the other…

A: Given: A flexible stretched string is constrained to move with zero slope at one end x=0, while the…

Q: 3. Verify the statement by showing that the derivative of the right side is equal to the integrand…

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Q: Find critical points of ƒ(x) = x² ln(x) — 1⁄x² on the interval (0, ∞).

A: Given; fx=x2lnx-12x2 ; x∈0,∞    As we know that; The critical points of the function, y=fx can be…

Q: Find a special solution of yn+2 - Yn= fo = constant by variation of parameters.

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Q: Calculate the truncation error to solve the differential equation: Yi+1¬Yi = Xị → (*) Ax dy Instead…

A: Follow the following solutions to get the complete correct answer.