19. Given the the function y =f(x), which of the following functions is obtained when the graph is stretch vertically by a factor of 2, then shift 1 unit downward? A) y= 2f(x – 1) B) y=f(x – 2) – 1 C) y=f(x– 1)+2 D) y= 2f(x)– 1

Q: 1. Differentiate G(x) = Ax+Bx+C 2. At what point on the curve y= 1 + 3e* – 3x is the tangent line…

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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: 7-The tangent of the curve x^2+y^2- 2xy3D0 at the point (1,1), is * O a. y=2-x. O b. y=x-2. C.…

A: We find equation of tangent to the curve

Q: 2. Show that the function u = e(xy) + VrY 4(y/x) provides the equation Pu = 0. dy? %3D -

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Q: 9. Find the constants a, b and c of cubic function f (x) = ax³ + bx + c such that : • The slope of…

A: Given that, f(x) = ax3 + bx  + c Slop of tangent line at x = 3 is 0. f'(1) = 24 f(x) croses the x…

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A: We have to find the direction A in which the given function decreases most rapidly.

Q: 9) Where is the function h(t) = (t + 5)"3 differentiable?

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 4. Find the equation of the tangent line to f = 10** at x = 0. А. у %3D 1 B. x = 1 D. y = x – 1 E. y…

A: Tangent line equation =>y – y1 = m (x – x1), where m is the slope and (x1, y1) is the coordinate…

Q: 4. Find if y is a function of r defined implicitly by da 2*y + sin a = xe" + In

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Q: 1. Answer the following questions: (a) Find the linear approximation of y- f(x)-Vr at a 256 and (b)…

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

Q: 7) What is the equation of the tangent line of f(x) = xe"+ 3, at x = 0 a) Y= x+3 b) Y= 3 c) Y=…

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Q: 3 36 Consider a fumetion f whose first and second derivatives are f'(x) and f"(r) = 5/2 (1r² + 1)"/2…

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Q: 4/(A)Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction. дz əz (B)If Z…

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Q: 11. Find the linear approximation to given function at indicated point (Баллов: 2) x2 z = 3 + +, Po…

A: Topic:- linear approximation

Q: 1. Any function y = f(x) can be expressed as x = f(y) in standard mathematical methods for solving…

A: Given: For any function y=f(x) can be expressed as x=f(y) in standardmathematical methods for…

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

A: direction of maximum increase  Let maximum rate of change of a function f(x,y)  occur in the…

Q: 1 A point is moving along the graph of the functiony = dy 9x2 + 6 such that dt = 3 centimeters per…

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Q: Find D,y, given y = 3e" (2x – 5)*. D.y = 3e [4(2x– 5)'(2)]+(2r-5)'(3e") = 24e" (2x – 5)' + 3e"…

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Q: Find the derivative of the given function at P. (3, 3, 3) in the direction of u = 3i + 4j f (x, y,…

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Q: 4. Suppose that F(t) is a differentiable function of one variable. Define the function z(x, y) = e'F…

A: z(x,y) ey F (exy )diff wrt xdzdx = ey F' ex/ye.1/yzx = ey.ex/yyF' (ex/y)and diff wrt ydzdy= ey…

Q: 19. The slope of the tangent to the curve (x2 + y²)² = 4.x²y at the point (1, 1) is 3 3 (a) - () – 1…

A: We have to find slope of the tangent to the curve x2+y22=4x2y at the point 1, 1. We know slope of…

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: 4-The area bounded by the curve y = 2x- r and the x- axis is 5- if y = x - 2r +4 and x = t +2 then…

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Q: 18. Use the Linear Approximation to f(x, y) = /x/y at (9,4) to estimate 19.1/3.9.

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Q: Consider the For at function y= In(x+1) . what valves" of x is y undefined ?

A: The given function is y=ln (x+1) We know that, for the function ln x, x>0

Q: 1. Consider the following function: y = f(x) = ln (2.x² + 6x +5), for r2 %3D (a) Calculate f'(0),…

A: The given function is y=f(x)=ln2x2+6x+5

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

A: Introduction :

Q: Q10. Expand f (x, y) = e" cosx about up to third degree terms by using Taylor's theorem for a…

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Q: -Determine the analytical function f(2)=u+iv if = y'. Is u(x, y) harmonic?

A: Let fz=u+iv Here, ∂v∂y=y2 We have to check whether ux,y is hormonic or not. Since, ux,y=u and vx,y=v…

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: If the derivative of the closed function x2 + 2x – 3y + y² +m = 0 at the point (1, 1) is available,…

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Q: 20. What is the equation of the tangent line of f(x) = Vx = 4? A. x - 4y + 4 = 0 B. x + 4y -4 = 0…

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Q: În 10 In 10 (2x- 7) 2 IH 10 Find the indicated tangent line. 17) Find the tangent line to the graph…

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Q: What is the equation of the curve y = ax* + bx + cx² + dx + e tangent to y = 25x (2,14), to y = 2x +…

A: By verifying options and substitution of point (-1,11) it is verifying option C

Q: It is given to you that an equation of the tangent line to the graph of y=g(x) at x=4 is 4x+7y=−54…

A: Given The tangent line to the graph of y=gx at x=4 is given by 4x+7y=-54

Q: 3. The cost C of manufacturing transformers in a factory varies with the output N per day according…

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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: (d) Suppose that y(x) is a function and that y(2) = 1. Let y² + y = x. Using implicit differentian…

A: The objective is to find y'(2)and find the equation of tangent line to y(x) at x=2.

Q: Suppose that the functions f and g, with linear approximations L, and Lz at x = a as shown below.…

A: Limit problem

Q: 3. Suppose that z = f(x, y) is a differentiable function with respect to variables !! x and y and is…

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Q: B. Suppose that Z = f(x.y) is given implicitly by an equation F(x.y.z) = 0. Prove that dz/ax =…

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Q: 1, Differentiate the function. (1) f(x)= /32 (2) f(x)= (x°+10) 5 (3) f(x)= 2.x - V х (4) f(x)=…

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Q: 1. Any function y = f(x) can be expressed as x = f(y) in standard mathematical methods for solving…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

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

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

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Q: 1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula…

A: Consider the curve F(x, y)=0. The objective is to show that if F has continuous second derivatives,…