Find the area of the region under the graph of the function f on the interval [1, 4]. f(x) х

Q: That the value of the integration g(1) = 00 , g(2) = 0 1-e t) -dt 9(t) where g is a function that is…

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Q: X- y – sin for its homogeneity. If it is homogeneous, give its degree. Test the function defined by…

A: For the solution of the problem follow the next step.

Q: Q4: Draw and Integrate the function f(x, y) = (xy) over the region bounded by the curve x = y² and…

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Q: A company's marginal revenue function is  MR = 110 − 20x1/3,  where x is the number of units. Find…

A: In order to find the revenue function, integrate the marginal revenue function.Integrate the given…

Q: Find the value of a so that the function f(x) = xe has a critical %3D point at x = =D3. NOTE: Enter…

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Q: 6. For the function f(x,y) = 8x³ – 12xy + y3 a) Find all critical points of f (x, y)

A: Solve all the three parts for the given function f(x, y)

Q: 1. Find the total derivative dz/dy, given (a) z = f(x, y) = 5x + xy - y2, where x = g(y) = 3y² (b)…

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Q: 2. Integrate numerically the given function, fx0.1(1.2-x)(1-e20(x-1)) dx with the multiple-segment…

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Q: Find the critical point of the function f(x, y) = 4e² – 3xe". Use the Second Derivative Test to…

A: Function in the given question is: f(x,y) = 4ex - 3xey To find critical points, we set the following…

Q: Values of function y(x) at discrete values of x for 0 <x < 10 are given in table. Using trapezoidal…

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Q: 4. Find the critical points of each function and use the Second Derivative Test to classify the…

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Q: Consider the R² – R function f defined by f (1, y) = 2² – 6x +3y² - . (a) Find all the critical…

A: For critical points we need to find first order partial derivatives of given function and substitute…

Q: Find the average value of the function over the given interval and all values of x in the interval…

A: fx=cosx,    0, π2 The average value is, 1π2-0∫0π2cosx dx=1π2sinx0π2=2πsinπ2-sin0=2π

Q: Let f(x) = x². a) Find the tangent line to the graph of the function at x = 9. y = b) Find the…

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Q: Find the critical point of the function f(x, y) = - (20x + 5y? + ln(]æ + yl)). c = Use the Second…

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Q: 2. Given f(x, y) = 12x2x³ + 3y² + 6xy. (i) Find critical points of f. (ii) Use the second derivative…

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Q: 4. Find the absolute extrema of the function f(x, y) = ry-x-3y on the triangular region with…

A: To find the absolute extrema of the function f(x,y).

Q: (1) Let f(r, y) = (x + y)e-=v. a) Determine the quadratic approximation function of f(r, y) at the…

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Q: Match functions ƒ with their antiderivatives F. F (x) = cos (11 – x) F (x) = -11 cos (x) F (x) = -…

A: use substitution method and product rule for finding the antiderivative.

Q: Q4) The critical points of the function f(x, y) = 8y³ – 12xy + x³ O (0,0) and (1,2) O (0,0) and…

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Q: Find the absolute extrema of the function on the closed interval. f(x) = 7x² + 2, [-1, 2] -(0,2…

A: The answer is given below:

Q: Find the critical point of the function f(x, y) =-(8x+2y2 +ln(|x+y|)). c = Use the Second…

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Q: Find the critical points of the functions S(x, y) = x + 2y – 4y + 8x, g(x,y) = x² – 14xy + y Use the…

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Q: Consider the function f(z,y) = kr?- 2ry +y?. %3D 1. Show that (0, 0) is a critical point of f(z, y).…

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Q: 4. For the function f(x) = x²/*(x – 1)4/³, find the x and y coordinates for all critical points,…

A: Givenf(x)=x23(x-1)43 To find critical points , stationary points and identifying its local extrema.

Q: Consider the following function. y = x2/5 (a) Find y' = f'(x). f'(x) = (b) Find the critical value.…

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: The integrating factor of the given DE are already given below. What is the value of "n"…

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Q: (a) Find the critical point of f(r, y) = (4x² – 3) (2² + 43y). (x, y) (b) Find the discriminant,…

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Q: f (x, y) = xª – 2.x² + y² – 4y + 5. a) Use the second derivative test to find the critical points b)…

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Q: Find the critical points for the function f(x, y) = x² + y³ + 2xy – 2x – 7y. (You do not need to…

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Q: Determine the equation of the tangent line to the graph of the function f(x)=x* – 4x atx = 3 . Also,…

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Q: 4. Find the critical points for the function f(x, y) = x² +y³ + 2xy – 2x – 7y. (You do not need to…

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Q: 3. Find the critical points of the function f(x, y) = 4x2 + 9y2 + 8x-36y + 24 and use the second…

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Q: t) Determine an antiderivative, y, of the given derivative, y. Then use the given condition on y to…

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Q: Find the critical point of the function f(x, y) = 9x 3y- - In(\r+ y|). c = || Use the Second…

A: Let f(x,y) be any function of two independent variables x and y supposed to be continuous for all…

Q: Match the function on the left to its appropriate antiderivative on the right. Prompts Submitted…

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Q: Q: Find a continuous function f (x) satisfying x*– 4x'<f(x)<2x -x' for all x e [0,2] such that the…

A: In this question we have given a relation and with the help of this one we have to find the function…

Q: Find the value of x which minimizes: 1 Use the Lagrangian method = [x*)dt min. J s.t. X 3D —2х +4…

A: Given: J=∫01x2dts.t.x˙=-2x+4x0=1x1=0

Q: Integrate the function f over the given region. f(x, y) over the region bounded by the x-axis, line…

A: Given: fx,y=1lnx From the given curves the bounded region is as shown below: Find the x-intercept:…

Q: approximation of I = [" f(x)dx using composite Simpson's rule with n=4 is:

A: In this question, we evaluate the definite integral by using the composite Simpson's rule for n=4.

Q: . Find the critical points for the function f(x,y) = x² + y³ + 2xy – 2x - 7y. (You do not need to…

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Q: The functions f(x, y) = x 2 + y 2 and g(x, y) = x 2 - y 2 both have acritical point at (0, 0). How…

A: We have f(x, y)=x2 + y2 and g(x, y)=x2 - y2 By finding the partial derivatives fx=2x, fy=2y, gx=2x,…

Q: Find the critical point of the function f(x, y) = 5x – 5y? – In(æ + yl). c = Use the Second…

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Q: Find the average value of the function f(x) = x³ – sin(x) on the interval [0, 7]

A: We Have to find average value

Q: ● If the pollution index of a point (x, y) is given by p(x, y) = x². Calculate the total pollution…

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Q: on Find the absolute minimum and maximum of the function f(x, y) = 2x¹ - xy² + 2y² the region 0≤x≤…

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Q: 1+x Find the approximation of dx using Simpson's rule with step size h = 1+x2 0.25.

A: Simpson's rule: numarical methods