Find the area of the shaded region. square units 2 + 1 -1 -²4 2 +3 y=x-2 3 4 y=√x

Q: Write the following expression in expanded form. (x+7)4 (X-5)√√x+4 In

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Q: A retail business owner wants to build two adjacent retail stores on a rectangular plot of land. The…

A: The figure

Q: Evaluate the following indefinite and definite integrals using substitution.  Show all work, thank…

A: use substitution method for solving such integral

Q: Suppose we are trying to show that lim f(x) = L where the graph of f (x) is given below. A distance…

A:

Q: (4) Find the maximum and minimum values of f(x, y) = xy on the ellipse x² - xy + y² = 1.

A: The given equation of function  Let

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A:

Q: (c) (d) (e) creasing? Does g(x) have any critical points? If any, identify all critical points. On…

A: Given: To Find: (c) To find the critical points if any of g(x).(d) To find the interval(s) on which…

Q: As with discrete-time dynamical systems, equilibria can act strange when the slope of the…

A: We have to graph a rate-of-change function that has a slope of 0 at the equilibrium but the…

Q: Use the zero, 5+ i, to write P(x) as a product of linear and irreducible quadratic factors.…

A: we need to write P(x) as a product of linear and irreducible quadratic factors

Q: A firm's marginal cost function is MC(q) = 5q¹ + 4q + 10. Find the total cost function if the fixed…

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Q: Find the indefinite integral. [9√ w dw = +C

A: We know that,.We have to find the integration of .

Q: A cell culture contains 4 thousand cells, and is growing at a rate of r(t) thousand cells per hour.…

A: Substitute t=5 in r(t) and solve, an then add 4 thousand to it.

Q: a(x,y) Solve the system u = x-y, v = 2x + 3y for x and y in terms of u and v. Then find the value of…

A: The system of equations  and   The function for x in terms of u and v is The function for y in terms…

Q: Find an antiderivative F(x) with F'(x) = f(x) = 6e² and F(0) = 4.

A: F′(x)=f(x)=6e2x and F(0)=4

Q: Find an equation of the line tangent to the graph of G(x) = 3e The equation of the line is y=. at…

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Q: Let F = 6xyi + 8y2j be a vector field in the plane, and C the path y = 72 joining (0,0) to (1,7) In…

A:

Q: Use the graph to evaluate the limit. lim f(x) X→0 6 Ay

A: Consider the graph

Q: Evaluate the improper integral O a.-2 O b. 1 042 C 3 X

A:

Q: Given the definitions of f(x) and g(x) below, find the value of g(ƒ(8)). f(x) = X 11 g(x) = x² + 7x…

A: The given functions  and .The aim is to find the value of .

Q: 5 (x-2) n²+1 n=1 Find the radius of Convergence R₁ of the series. Find the interval of convergence,…

A: The given series is summation of(x-2)n/(n2+1), n from 1 to infinity.

Q: The cost C (in dollars) of building a house is related to the number k of carpenters used and the…

A: The objective of the question is to understand the effect of increasing the number of carpenters and…

Q: F(x) F(2) (5) F(7) - L² (t³ + 6 t F(x)= (t³ + 6t-5) dt

A:

Q: Problem #8: Use Divergence theorem to find the outward flux of = (3x², e¹², cos³ (1² + x)) of the…

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Q: Write v as the sum of two vectors, one in Span {u₁) and one in Span (u₂,43,44). Assume that…

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Q: Find the exact location of all the relative and absolute extrema of the function. (Order your…

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Q: Given the graph of the function f(x) below, estimate the slope of the tangent line to the curve at x…

A: The graph of the function  is given as,Estimate the slope of the tangent line to the curve at

Q: The grid on the right shows the graphs of several functions f(x) whose slope at 8x each x is Find…

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Q: Find the intervals on which the graph off is concave upward, the intervals on which the graph off is…

A: The objective of this question is to find the intervals on which the graph of the function f(x) = -x…

Q: Find an antiderivative of the function f(x) = 5x - √x.

A: f(x)=5x−x

Q: Find an equation of the tangent line to the graph of the function at the given point. y = 4 − x² −…

A: y=4−x2−ln⁡(12x+1), point (0,4)

Q: Question 1 (i) Determine dy/dx in the following: (ii) y = cos(x³ - 2x) y = x²-2 sin x y² −2(x+y)+x²…

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Q: Find the area of the region between the curve and the x-axis. f(x) = 16-x², from - 7 to 7

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Q: Biologists stocked a lake with 300 fish and estimated the carrying capacity (the maximal population…

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Q: A jewelry box with a square base is to be built with silver plated sides, nickel plated bottom and…

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Q: •3 L₂(³- -2 - (3 - x) dx

A:

Q: Evaluate the following integral. 2 | (0²-0 -2 (4y -6y+6) dy

A:

Q: Find all the antiderivatives of the following function. Check your work by taking the derivative.…

A: Given,

Q: When Abraham jumps into the air, his height in feet above the surface of the water is given by h =…

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Q: (f) (g) Find the absolute maximum and absolute minimum of g(x). On what interval(s) is g(x) concave…

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Q: Determine the integral by making the appropriate substitution. . 1 -dx 8x 1+ 4e

A: .

Q: Evaluate each expression using the graphs of y = f(x) and y = g(x) shown below. a) (gof)(2) b)…

A: To evaluate each of the following expression by using the graphs of  shown below.

Q: Find the equation for the plane through Po(-6,8,8) perpendicular to the following line. x= -6+t,…

A: We find the equation for the plane through P0(-6,8,8) perpendicular to the following…

Q: Evaluate the following. log 6216

A: Let .We know that,

Q: I had that first answer but it was wrong and I also had 2 sin theta cos theta but as my second…

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Q: Find the average value of h(x) over the interval [1,7] given that g (z)=-6x + 8. Edit View Insert…

A: Given,

Q: Estimate the area under the graph of f(x) =3x² + 12x + 14 over the interval [0, 3] using five…

A: To estimate the area under the graph of  over the interval  by using five approximating…

Q: Use the graph to evaluate the limit. lim f(x) X→-1 X G

A:

Q: The price-demand equation for a particular flashlight is given by p= 114 -0.004x, where x is the…

A: We need to find consumer and producer surplus.

Q: For Evaluate the following expression. Select the correct answer below: f(x) 4-x-x² ifxsl 2x-1 ifx>1…

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Q: 1. A rock is thrown upward with a velocity of 20 meters per second. Its height, in meters, t seconds…

A: According to our guidelines, we can answer only first question (due to multiple questions). Kindly…