O Caloulat 2nd hounene f(x)= sT こ>×ラ0 2. う2×23 With flx)> f(x+3n) Yne 忍

Q: he Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 5+x2 Ciuo Hooim

A: Here we have to use linear approximation rule.

Q: Consider the function f(x) = 2x10 + 7x° – 6x² – 9. Enter the antiderivative of f(x) -

A: To find The anti derivative of f(x).

Q: Find the general antiderivative of f(x) = 23x + 14x-2 and check the answer by differentiating.…

A: Given:- f(x) = 23x+14x-2 To find:- Anti derivative of f(x)

Q: Which value of c satisfies the conclusion of the MVT for the function f(x) = 3x² – 3x + 7 on the…

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Q: 4. If f(x)dx = (x + 1)ln(|æ|) + C, what is f(x)? (To write absolute value, write abs(x). Do not…

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Q: Prove that = va² – x* if y =(f)sin~+ () + (9)v&* - x²

A: Differentiation wrt x

Q: Suppose that f(x) is an antiderivative of f(x) = V1 + xt. Express JoV1 + x* dx in terms of F and…

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Q: Estimate the value of f, (1 – r 4.r + 2x) dr using single application Simpson's 1/3 Rule.

A: This is a Numerical Analysis problem.

Q: If fCx) is bdd Junchion an f(x) dx = の-3 then 3. True or Fal se ?

A: Solution :- An odd function is defined such that f(−x)=−f(x)

Q: Use the linear approximation of f(x) = /2x - 3 about c = 2 to estimate the value of V1.32 Enter your…

A: Given that: f(x)=2x-3

Q: Find linearization L(x) of f (x) = Vx at a =4 and use to approximate 7.8.

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Q: 4: Find the approximate value of f(-2.001, 1.002) where f(x, y) 3x?y + y? – xy +1

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Q: Use the Trapezoidal Rule with n-6 to approximate. f(x)=sim2x.a=0,b=π

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Q: find the fun Ction Y= f(x) that satisfies hp Jメ 8x² + 7 , 7, F (0) = -13 コ

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Q: Suppose that f(x, y) = yvx* + 1 on the domain D = {(x, y) | 0 < y < x < 5}.

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Q: If f (x, y) = Vr³ + y³ In(x² + y²)e*in (zy+y') + x³y+ 10 , then f. (1,0) =

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: 2. Find frxz for f(x, y,z)= z² e³xy

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Q: (b) Suppose that f(x) = SBx? – 3 if if xS2 (Bx+ 2 %3D Find the value of ß so that f(x) is continuous…

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Q: 4. Why is f'(x) approximated well by the difference quotient when Ax is very small?

A: Derivative of function f by definition is: f'x=lim∆x→0fx+∆x-fx∆x This is the difference quotient…

Q: Show that a fuinction F:R>R defired by 3 If I=y=0 1S continous ert (o0)

A: Continuity: Let a function f(x,y) be defined on an open disk B containing the point (x0, y0). A…

Q: x - y -2x Prove by definition that for f(r, y) fy(x, y) = %3D x+ y' (x+ y)2

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Q: Suppose J. 3sf(x)s5 for 2sxs8, how small can f (8) possibly be if f(2) = 10? State necessary…

A: Given that         3 ≤ f'(x) ≤ 5  for  2 ≤ x ≤ 8 Here we have to find how small value of f(8) can…

Q: Find the general antiderivative of f(x) 3 – 4x* + - 5VT x3 Preview 2.

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Q: .Determine if F(x, y) = (2xy + y-2)i + (x² – 2xy-3)j for y > 0 is conservative.

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Q: For f(z) = 2z', find ip using the definition,

A: The limit definition of a derivative of a function, f(x) at a point, x=a is given by .

Q: of of and ду For the function f(x,y) = In (7x + 9y), find

A: The given function,     f(x,y)=ln7x+9y

Q: of Let f(x,y) = xy° +7. Evaluate at (x,y) = (-7,1) and interpret the results. ду -

A: In this question we have find δfδy at (x, y)=(-7, 1)

Q: Which value of c satisfies the conclusion of the MVT for the function f(x) = 3x² – 2x + 3 on the…

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Q: af AMPLE 3 If f(x, y) = sin). calculate and 5 + y ax LUTION Using the Chain Rule for functions of…

A: Solution of the problem as follows

Q: Let f(x)=6x2+1f(x)=6x2+1.Enter an antiderivative of f(x) . . .

A: The given function is,

Q: 2. Let f(x) = r³, 0, if reQ if r ER\ {Q} Show that f'(0) = 0.

A: We have given a function ,  fx = x3 , x ∈ ℚ0 , x ∈ ℝ \ ℚ We need to show that , f'0 = 0 We know the…

Q: - x'yt, show that fxy = fyx. 7,4 Given f(x, y) = et*

A: Given f(x,y) = e(x^4y^9) - x7y4

Q: 1. Can Rolle's Theorem be applied to y = (x – 2)5 on the interval [0, 4]? Justify.

A: we will see how to proceed

Q: The antiderivative of the function 4 + 10x is. x2 f(æ) = 4 + 5.0x2 + c - -4 5.0x2 + c -10 + 2.0x2 +…

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Q: The range of the finction f(x, y) = In(-x² -+1) is %3D None of these O (00:0] O [0; +0) O [0;1]

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Q: 19 Suppose that Ts Cx) centered at 2 for f (x) is gicn by Ts Ca):345Ca-2)+5 Cx-2)?ょ2x-2)+(x-2) Than,…

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Q: rsin 28x /ī+ t² dt and If f (x) = So g (y) = ' f (x) dæ., what is g" (6s )? 168

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Q: what is the antiderivative F(x) 0f f(x)=3x^((1)/(2))-x-1that satisfies the condition F(4)=0 A,…

A: Given that:f(x)=3x1/2-x-1, F(4)=0

Q: Use local linear approximation based on the input 1, to estimate f(1.41) when f(x) = x5+26x³ – 112x…

A: Use linear approximation formula:-

Q: Find the value of K that makes 4-x2 f(x) = {2-x if x # 2 2K if x = 2 continuous at x = 2 ?

A: Find the value of k

Q: The range of the finction f(x, y) = In(-x2-+1) is %3D None of these O (-00:0] O [0; +0) O [0;1]

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Q: If f (x, y) = Vr3 + y3 In (x² + y³)esin(zy+y') + x°y+ 10 , then f. (1,0) O 4

A: Properties of derivative  ddxex=ex ddxxn=nxn-1 ddxsinx=cosx ddx(lnx)=1x

Q: For what values of a and b is ax + 2b, g(x) = {x? + 3a - b, 0<xS2 3x 5, %3D - continuous at every x?

A: The given function is gx=ax+2b,        x≤0x2+3a-b,  0&lt;x≤23x-5,           x&gt;2. For the given…

Q: Q3) For what values of a and b are ax + 2b , y = x2 + 3a -b, 3x-5, 0 2 Continuous at every x ?

A: We will check continuity at breaking points of the function. For continuity , left hand limit and…

Q: inh´x + cosh²x = 1 = x²arccsch(x²) then f

A: 1. The function fx=y=coshx is represented as , coshx=ex+e-x2 To check whether the function is odd…

Q: Suppose that a function f(x, y) satisfies fxx fyy – (fxy)² > 0 at a point (a, b). How is the sign of…

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Q: Find values ofa and b that make B(x) both continuous and differentiable at x = 2: ax? B(x) ={ 6x + b…

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