Below is a graph of y = f(x): 1 -1 -2 -3 1 2 3 45 67 8 Use this to compute 2. | f(x)dx

Q: For each of the following exercises, a. decompose each function in the form y = f(u) and u = g(x),…

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Q: I) Consider the function: y = + C,e2x + C,e-5x + Czxe-5x

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Q: For f(x) = e+cos(x), calculate f (0) by using the chain rule!

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Q: For what values of z does the graph of f(z) = 21 – 9z² – 60z – 1 have a horizontal tangent line?…

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Q: For what vaļue of x does the function g(x) =x - 2x? strictly convex? В. x> 0 A. x> 2 D. x -2

A: From the given problem:   gx=13x3-2x2   As we know that:   If f''(x)<0. then function strictly…

Q: Find the function y(x) satisfying dx2 = 12 - 12x, y'(0) = 5, and y(0) = 8. ay = 12- 12x, y'(0) = 5,…

A: an initial value problem  is an ordinary differential equation together with an initial condition…

Q: Consider the function 8 · + 9. xy f(x, y) In which direction does the function f(x, y) increase most…

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Q: Assuming that y is a function of x, differentiate x^9y^5 with respect to x. Use D for dy/dx in your…

A: by using chain and product rule of differentiationddx(x9y5)=9x9-1y5++5x9y5-1y'

Q: The derivative dy of the function y = f(x) with dx f (x) = e' (1ª + 2t³) is a) e' (41³ + 61²) + e'…

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Q: – x®y³, 6. Given f(x, y) = e®° - show that fxy = fyx.

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Q: If the graph of Y=f{X) contains the point (0,2), dy dx and f(X) > 0 for all X, then yet? f(x) =

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Q: For the function, evaluate the following. (If an answer does not exist, enter DNE.) exyz g(x, y, z)…

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Q: IF THE CURVE OF THE FUNCTION F (X) = Y PASSES THROUGH THE TWO POINTS (2,2) AND (1, K) AND SATISFIES…

A: We have to solve given problem:

Q: d*y 4. Find 5 of the function f (x) = - e dz"

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Q: Given: f(x, y) = arctan Find: F ƒ(x, y) dxdy x² - y² (x² + y²)² 3²-x² (x² + y²)² -y³ (y³ + xy²)² y²…

A: Given: fx, y=arctanxyTo Find: ∂2fx, y∂x∂y

Q: The graph of y = f(x) is given below: 3 2 -3 - –1 2 3 4 5 6 7 (x)dx = 4.5, then f(x)dx =

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Q: Use differentials and the graph of f to approximate (a) f (1.9) and (b) f (2.04). To print an…

A: To calculate the approximate value of a) f(1.9) and b) f(2.04)

Q: Find the length of the graph of ; a. f(x)=⅓x2 -⅔ between x=2 and x=3.  b. x=cost, y=sint from t=0…

A: See the detailed solution below.

Q: Given the function: f(x, y) = y°e -5x a. Find fyy(x, y) b. Find fyyæz (0, 1)

A: a)f(x,y)=y3e-5xPartial differetiate w.r.t yfy(x,y)=3y2e-5xPartial differetiate w.r.t…

Q: For the given function find dy/dx. x- y' | = x + 2 y+ x2 1- x-3y-4x 3x2 + y + 2 y' 1- x + 3y - 4x y…

A: x-y3y+x2=x+2

Q: Given the graph of f(t) below, f(t) dt = 0. %3D

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Q: Suppose C is the graph of y = f(x) for a < x < b. Compute x dy + y dx in terms of f.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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A: (i)  From given graph, the values of x increases as y decreases. So, dydx&lt;0. The derivative can…

Q: - Find F-T: for the functions -at e t70 1at tco e

A: We have to use integral formula.

Q: tiny, no bug lands on a piece of graph paper and walks along a path so that t minutes after it…

A: Increasing function

Q: For the function y df-1 f(x) = a? – x + 2, x > 0.5, find dy y=10 (f-1)'(10).

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Q: If we use trapezoidal rule for a function f(x) = x +2 1 - , then the approximate of J f(x)dx is…

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Q: %3D 42. Find f(x) dx for each graph of y = f(x). (a) y. (b) y 2. 1. 3 aronh of flr) = 2x + 3 and

A: Given query is to find the valuebof intgy from the graph.

Q: Given the equation x+xy-3y = 0, evaluate Assume that the equation implicitly defines y as a…

A: The equation is given by x3+x2y-3y3 = 0                                       .......(1) To evaluate…

Q: 3 Let f(x) = 8x° 1 df 15x - 5, x2 1.5. Find the value of dx at the point x= 2004 = f(7). %3D

A: Known fact: derivative of f-1x=1f' f-1x.

Q: f(x,y) = x/3 – x/3y² is harmonic? Does the function

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Q: The value of b makes the line y = 2x +b be tangent to the function f (x) = x² is O -1 none О 1 O 2

A: Tangent line related problem......

Q: For the functions below, what is the direction of fastest increase at  (1, 1, 1)? (a) f(x,y,z) =…

A: The direction of fastest increase for a function at a point is the direction of the gradient of that…

Q: First write the function y = Vx2 +1 as a composition of y = f(u) and u = g(x), and then dy apply…

A: y=x2+1y=f(u), u=g(x)To find:dydx

Q: dy Q1: - Find of the following functions dx y = (x +) (x –+ 1 a. %3D - x2+3 b. y = %3D (x-1)3+(x+1)3

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Q: Find the linear approximation to the function. x2 f(x + Δx) ≈      Evaluate it at the given…

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Q: I grad(f)•dr where C is graph of y = x² + 3x from (0,0) to (2, 14) and f (x,y) = ev/lx*•1}

A: The function is fx, y=eyx+1. Find: ∫Cgradf·dr…

Q: Given the function(x) = x3+ 1, find the ∆y, dy, ∆y-dy

A: f(x)=x3+1

Q: plve the following initial value problem for y as a function of x. dy 3X dx = Vx2 - 4, x2 2, y(2)= 2…

A: 3xdydx=x2-4 multiply both sides by dx 3x dy=x2-4 dxdivide by 3xdy=x2-4 3xdx Now integrate it on both…

Q: Give an example of a linear function f(x)= mx + b, with m,b ±0 and an interval a<xsc where f(x)dx=0…

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Q: Suppose that a function f(x) takes the following values: 1 3 f(x) 2.4 2.0 3.5 5 Calculate the…

A: The Trapezoidal Rule formula with n=2 subintervals is written as T2=∆x2fx0+2fx1+fx2 where…

Q: use the graph of y=f(x) to graph g(x)=-f(x-1)-1 given the coordiantes (-4,0) (-2,-2) (0,0) (2,2)…

A: we have been given the coordinates (-4,0), (-2,-2), (0,0), (2,2), (4,0) for the graph y=f(x) first…

Q: Solve the following initial value problem for y as a function of x. dy X- 3Dx? -9, х23, у(3)%3D0

A: By using integration formulas

Q: 1. y = u=x? + 1 2. y= www v 3. y3D u? + 2u -3; u = Vx

A: We have to find derivative y by using chain rule.

Q: 18 Find | f(x) dx for each graph of y = f(x). (a) 20- (b) AY 20-

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Q: For the function y = x² + 2x, the value of dy when x=3 and dx=0.1 is (А) 0.15 B - 0.8 -0.15 D 0.8

A: The given function y=x2+2x  ;  x=3 and dx=0.1

Q: Let f(x) = cos x. Sketch the graph of y = 2f (3x – 4) for 0<x < 67.

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Q: 2. Sketch the graph of the function (a) f(x, y) = Vr² + y? (b) f(x, y) = Vx² + y? – 1 %3D

A: Given a. fx,y=x2+y2b.fx,y=x2+y2-1

Q: y? For function f (x, y) x2+1 Starting from the point (1, 2), at which direction does the above…

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Q: Sketch the graph of h(t) = |t| + |t + 1|

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