Q2: Using Theorem 3, find f(1) if L(F) equals: 1 28. (s + V2)(s - V3)

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

A: Differentiation wrt x

Q: 2. Find a function f(r, y, 2) which makes (yz?, rz?, f(r, y, z)) conservative. Show that your answer…

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Q: Maximize Q = xy, where x and y are positive numbers such that x+3y 16. The maximum value of Q is and…

A: Maximize Q=xy, where x and y are positive numbers such that x+3y2=16

Q: Determine two functions, defined on the interval (−∞,∞)(−∞,∞), whose Wronskian is given by…

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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: 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 derivatie: F (+2 %3D (-t*+*z+)た =人

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Q: 2. If F(x, y, z) = 2z3 – 3(x² + y²)z, then verify that Frx + Fyy + F2 = 0. %3D

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Q: Use Euler’s method with n = 2 on the interval 2 ≤ t ≤ 3 to approximate the solution f(t) to y′ = t -…

A: Given, y'=t-2y y(2)=3

Q: Calculate f. x²dx + xydy where C consists of the straight line segment from (0,0) to (1,1), followed…

A: Proceed as shown below

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: Use the Linear Approximation to estimate Af = f(4.8) – f(5) for f(x) = x – 5x². (Use decimal…

A: Given data:   The given expression for the function is f(x)=x-5x2. The given value a=5.   The…

Q: Find the interpolating polynomial of degree two for f(x) cos(r2) +r on the interval [-1, 1] using…

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Q: of of and ду Find f(x,y) = Vx + 3y?

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Q: 3. Consider f : R2 → R defined by f(x,y) = y³ + 3x²y – 6x² – 6y? + 2. - (a) Determine the critical…

A: The given function is: f(x,y)=y3+3x2y-6x2-6y2+2

Q: Show that the function f : [0, 1] →[0, 1] given by f(x) = (x −1)2 has a fixed point. Can you apply…

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Q: 6) If y=x² +1+ f dt , prove that y"= 2 - x2

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Q: How do you evaluate the limit as t approaches 0 (1/t*the square root of 1 + t  - 1/t) with the…

A: Obtain the value of limit as follows.

Q: Find the local linear approximation of f(x)= at 2+ x xo = 2, where Ax = x – 2. NOTE: Enter the exact…

A: while finding out the local linear approximation of any function f(x), what we do is to determine…

Q: Find a point zo where the function f (z) = (z – 8 – 10i) (z – 8 – 10i) is differentiable. What is…

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Q: Find the linear approximation of f(x) = (5 + x)n at x = 0. Use the approximation to estimate the…

A: fx=5+xn at x=0. Differentiating with respect to x, we get f'x=n5+xn-1 Now, f0=5+0n=5n &…

Q: Find a linear approximation of the function f(x) = V1-x at a = 0. %3D

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Q: Find fg, fyand f; if f(x,y,z) = x - Vy² + z²

A: Given:     To determine: Partial  derivative  fx, fy, fz

Q: (a) find the local linearization of f(x)=fourth root(x) at x=16 (b) Use the linearization to…

A: It is a linear approximation problem

Q: Show that f(u, v) = (u – 2) (v + 3) has neither local minima nor a local maxima at (2,-3). %3D

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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: Find the zeYo k its ovdev for Sunction f2)=1-Ti + Z+ e.

A: Given the function, f(z)=1-πi+z+ez. Now, in order to find the zero of the function f(z), we will…

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: Find the best linear approximation, g, to f on the interval [0, 1]. (x) = 2/x g(x) %3D

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Q: Find the particular sölution f"(x) = 4, f'(2) = 12, f(2) = 17

A: integration 2 times and after applying initial condition we get f(x)

Q: 2. Find whether the function F-(* - y' )i + (v² - 3x)j + (:² - xy is irrotational.

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Q: der to evaluate t son's 1/3rd rule e used at x = 0.C of the error of

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Q: | f(t) dt 20z 4, then f (t) dt is If 4x²+21

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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: Q, Frd the donain of H fallowing function: fa) = 5x -3x-4

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

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Q: Find the linear approximation of f(x) = Vx-1 approximate 2.02. near a = 2. Use the result to

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Q: 3. Use the Intermediate Value Theorem to prove that the equation x-5x = 4 is solvable on the…

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Q: Suppose that f(0) = 1, ƒ(0.5) = 2.5, f(1) = 2, and f(0.25) = f (0.75) = a. Using trapezoidal rule…

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Q: Integrate from f(x) = x4 from 0 to 1 by (Trapezoidal Rule) with h = 1, h = 0.5, h = 0.25 and…

A: Here, f(x)=x⁴ So, I=  Integrate from f(x) = x⁴ from 0 to 1. Now we can solve by Trapezoidal rule,…

Q: Find f fy. - f(x.y.z) = x - Vy² + 22? + 2z² = (Type an exact answer using

A: Here we have to find fx , fy and fz  of

Q: Find a function f(x) whose linearization would help me come up with an approximation to 4 26

A: We want to find the function,  It's form is ,L(x) = f(a) + f'(a) (x-a)  We approximate 4/26 ~ 4/25…

Q: 2. Use the secant method to estimate the root of f(x) = a° + a³ + 3. %3D By starting with the…

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Q: Q3: Find fxx of the function f (x, y, z) = -In/1-x2 - y2 – z2 %3D

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Q: Find the 2nd solution using reduction of order. xy" +y' = 0; y1 = Inx For the toolbar, press ALT+F10…

A: Just I have used the method of reduction of order and solve in detail and find that  Second solution…

Q: At what x-value(s) on the interval [-2, 3] does the graph of f (x) = x² + 2x – 1 satisfy the M.V.T.?

A: According to mean value theorem,Let f be continuous on [a,b] anddifferentiable on (a,b). Then…

Q: Use the linear approximation to ƒ(x, y) 12x² at (3, 9) to estimate f(3.1, 8.8). y2+7 (Use decimal…

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.