10- Compute the following estimate of J f(x) dx using 8- the graph in the figure. M(4) 6- 4- 2- 0- 2. Using the Midpoint Rule, M(4)=

Q: Compare the values of delta y and dy for the function f(x)= x^3 - 3 at x=3and delta x= 0.2

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Q: 1.If f(x,y) cos(4x-2y)+ln(y² -2x) find £xy fx fxy,

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Q: 2. Show that the function u = p(xy) + Vry (y/x) provides the equation y². 0. dy?

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Q: 2. If f (x) = Sn* et? 0, dt, find f'(x) V2t+sect

A: The solution is given as

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Q: 2²y. 3. Consider the function f(, y) =

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Q: 26. Approximate V50 using Ay f'(x) Ax.

A: Step ILet  y = f(x)Let ∆x be a small change in x and ∆y is correspoding change in y. As ∆x is a very…

Q: Q11 Determine all the critical points for the following- S(x) = sin'x- cosx On the interval (0, 2n).

A: Given , f (x) = sin2x - cos x  (.) Definition :  Then critical point of a…

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A: Firstly, we will calculate f'(x), then f(a), f'(a).

Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: 8. Find the extremum and saddle points of the function f(x, y) – x3 – 3xy + y3 if any.

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Q: 4) Consider the function 9 defined by g(x, y) = cas (7X Jj ) + logg(x-y) does 9 ha ve the maximum…

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Q: Q2/ Find the orthogonal trajectories of the family of curves x-y - c² YAS

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Q: For the given function 9 = x-yz and 62 -(@C) at C= 3x?yi+ yz²j- xzk, Find 5yöz бубz point (1, – 2, –…

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Q: 2. Show that the function u p(xy) + Vry (y/x) provides the equation = 0.

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Q: Verify the final value theorem of f(t) =1+et[sint + cost]. O- 1 1

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Q: 3. Find the interval on which the curve of y= 2 1+3t+t² dt is concave up.

A: Second derivative is positive.

Q: of For the function f(x.y) = In (x + 6y), find- of and dy

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Q: Find the linearization of the function given below at the specified p f(x) = 4 In(x) at a = 1 L(x) =…

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Q: 4. Find the orthogonal trajectories of the family of curves y=Ce*™ +10

A: We have to find the orthogonal trajectories of the family of curves

Q: 8 Ay 10- Compute the following estimate of f(x) dx using 8- y = f(x) the graph in the figure. 6-…

A: Consider the graph of the function

Q: find the solution of following derivative by Runge-Kutta method f(x,y) = -2x3+ 12x2 - 20x + 8.5 let…

A: Consider an initial value problem dydx=f(x,y) with the initial condition yx0=y0. Then Runge-Kutta…

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Q: - The antiderivative of f (x) =; whose graph passes through the point (C 3+5sinx+. +3cosx 1(. 5 1(.…

A: Introduction :

Q: Ay 10- Compute the following estimate of J f(x) dx using the graph in the figure. 8- S(4) 6- 4- 2-…

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Q: Previous Question 8. Compute the following estimate of 10-1 f(x) dx using 8- the graph in the…

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Q: 8 Ay 10- f(x) dx using Compute the following estimate of 8- the graph in the figure. 6- S(4) 4- 2-

A: The given graph is  To find ∫08fxdx using Simpson's Rule with n=4

Q: Q2- If Z = f(x, y) = sin(x³y5) Find fyy and fyx

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Q: - Use Euler's method to estimate y(3) given y(0) = 1, and y' = x -. Use steps of h = 1

A: use euler method for finding the y(3)

Q: -2 In(x) Consider the function f(x, y) 3y

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Q: - Given f(x, y, z) = x In(yz³), find fzy and fyz.

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Q: 24.) Given the function f(x)=x²– 2x Estimate J f(x) dx using four subintervals by . finding R4, L4…

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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: Find the length of the curve between the specified interval: 3/2 a. y = x7² from x = 1 to x = 4 b. y…

A: (a) Given curve: y=x32 Interval x=1 to x=4 The length of the curve is given by the formula:…

Q: Find all critical points of the following function. f(x,y) = 10x²-5y²

A: Please see the below picture for detailed solution.

Q: 4. What is the maximum possible error if T4 is used to approximate | f(x) dx f(x) dx

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Q: 3 Q1// :- find fy,fy at point (4,1) for f(x,y) = Xe

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Q: Consider the following function: f(r) = 2r + 3z² – 12z Find the critical numbers of f. (x = ?)

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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: Find the standard (slope-intercept form) eq at the specified points. 1. f(x) = 3x² – 12x +1 at…

A: 1) Tangent line of the function f(x) at x1,y1 is given by y=f'x1x-x1+y1  3x2-12x+1 at P(0,1) x1=0,…

Q: 5) a) Compute Ko for the function f0=V+X by using the de finition of the deniratire, b) Find the…

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Q: Show mathematically that MRS is increasing for U=1-ex +e2y and is diminishing for U=lnX +LnY

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Q: Which of the following curves have critical points at x=2 and x=-2 * f(x) f(x) = 12 + 4x + 4 x2 – 4x…

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Q: 3. If f(x) = (1–- t²)e*dt, on what interval is the curve y =f(x) upward? concave

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Q: 4.1 Use the trapezoidal rule to find an approximate value for V1+x'dx with n = 4.

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Q: Calculate the error of approximation E, for: f(x) = v3x + when x = 8. Ax = dx = 0.1

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Q: Use the Quotient Rule to compute the following: t2 + 1 at t = -2 dt \ t2

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Q: 1. Use the Gauss forward formula with xo = 2.0,h = 0.15, n = 7 to find an estimate for f(2.5) if %3D…

A: Given: fx=xlnx. x0=2.0, h=0.15, n=7.   We can solve this by using Gauss forward formula