Find the area of the region bounded by the graphs of the given equations. y = 7x², y = 7√x

Q: Find the average rate of change of the function f(x) = Average rate of change = Give exact answer!…

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Q: The vector w = ai + bj is perpendicular to the line ax + by = c and parallel to the line bx - ay =…

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Q: 4. The graph represents the reciprocal of which quadratic function? 6-4 ya 2 on! N + Ny 10 A…

A: The graph of the function is given and We have to find the graph represents the reciprocal of which…

Q: Find the required higher derivative. Show your complete solution. 11. x=a²bsin 2at y=ab² cos 2at ;…

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Q: 2 2xy dy = y² – 2x³ dx

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Q: For the function f(x)=x²-9, evaluate f(x + h). 2 f(x + h) = | 21

A: Given, f(x)=x2-9

Q: B. Integrate the following functions: iii. ₁³4x³ +9x² + 2 dx

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Q: Of all possible right triangles with area 1, determine the one with the smallest hypotenuse.

A: This is an optimization problem, we find the critical points and use second derivative test.

Q: 4. Which of the following quadratic equations has no solution? a) 2x² - 4x = 2x - 3 b) 2x² - 15x…

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

Q: The function given by f(x) = x³+4x² + 1 defined on the interval [-3, 2] has absolute maximum of

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Q: f (x + y) dA, where D is the top half of the unit disk with the center at the origin.

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Q: What is the slope of the line that passes through the points (7, -9)(7,−9) and (6, -11)(6,−11)?…

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Q: 4. An athletic -equipment supplier experiences weekly cost of C(x) = x³ +40x + 700 in producing x…

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Q: Find a and b so that f(x) is continuous if f (x) 0 a = b a = − 14/1/2 O a = = -1/16 a= 96 b= b = =…

A: NOTE: Refresh your page if you can't see any equations. . the given function is

Q: Ty++F=o

A: Please see the below picture for detailed solution.

Q: Given that f(x)=√√x²-4 and g(x)=√√√4-2², what is the domain of f(x)+g(x)? OR O [-2,2] O {-2,2} None…

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Q: On which intervals is the graph of f(x)=2x4-12x² concave up? None of the choices. (1,+∞) only (-∞,…

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Q: 5. k(t) = -5t²e-4t + sin(31)

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Q: If ƒ(x) = x² + 6, g(x) = x − 3, and h(x) = √x, then (fog)(x) = (gof)(x) = (hog)(x) =

A: The given functions fx=x2+6, gx=x-3, and hx=x. We have to find the functions f∘gx, g∘fx, h∘gx.

Q: 23 Match the equations listed in parts (a)-(d) to the graphs in the ac- companying figure. a. y = (x…

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Q: Find the equation of the plane that passes through the point (1,0, 3) and is parallel to the plane…

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Q: If ƒ (x) = x³ − 3x + 5, find (ƒ−¹)′ (x) at x = f (2).

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Q: (2) If g(x)=√x+x²+1 In(t) dt, then g'(x) = (A) (4x³ + 2x) In(x4+x² + 1) - 2x ln(x² + 1) (B)…

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Q: A radioactive material is sampled from a site of leakage. In 2020, the amount of radioactive…

A: Let initial amount present in 1975 = x0Law of Decay x = x0e-ktk = constant t = time x = amount at…

Q: Given the vectors u, v and w in R³, which of the following calculations could result in the answer…

A: Given: Vectors u, v and w in R3. Final answer of Operation should be 3. Cross product of two…

Q: 1. Find by double integration the volume of the solid generated by revolving about the x- axis the…

A: According to our guidelines , we can answer only first question. Kindly re-post other remaining…

Q: Find the required higher derivative. Show your complete solution. 11x² 2 8. y=8x³-7x¹ −5x³+ -x+10;…

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Q: Consider the curve defined by the equation y — sin y = x − 1 for 0 ≤ y ≤ 2π Find d²y/dx² in terms of…

A: Solution: To find the second derivative of y with respect to x, we need to first find an expression…

Q: 2. Find the interval and radius of convergence of n=1 (-1)" (x - 2)" n2n

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Q: shouldnt e=2.71?

A: Yes, Value of e = 2.718

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 7t, y = 5…

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Q: Repeat the approximation using left endpoints. Ln =

A: Given f( x ) = 1x + 3 [ -2 , 3 ]

Q: x* (8) √**+/+ x2 dx =

A: To evaluate the given integral

Q: Question 2 Find all the points on the curve x²y² + 2xy = 3 where the slope of the tangent is -1.…

A: The given curve is: x2y2+2xy=3 To find all points on the curve where the slope of the tangent is -1…

Q: Find an equation of the plane through (4, -2, -8) that is perpendicular to the line x - 2 = 5t, y +…

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Q: Sarah can bicycle a loop around the north part of Lake Washington in 2 hours and 50 minutes. If she…

A: Given : Sarah can bicycle a loop around the north part of Lake Washington in 2 hours and 50 minutes.…

Q: Find a and that solve the vector equation: + ß ;) = (³) 3

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Q: 7. The volume of the paralleliped with corresponding vectors (2, 1,0), (-1,2,2) and (0, -2,1

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Q: Find the components of P, the position vector drawn below, given that ||P|| = 6.4. 2 2i + 3j + 5.29k…

A: Let's find new notations.

Q: Find an equation of the plane through (-1, 9, - 8) that is perpendicular to the planes 5x = y + z =…

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Q: Recall, the continuous exponential growth or decay model is A(t)=A0ekt, where A0=A(0) is the initial…

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Q: 6. (14 points) f(x) = xe-¹² (a) Find the critical numbers of the function f(x) (b) Find the absolute…

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Q: Find the solution of the exponential equation 7e* - 19 = 6 The exact solution, in terms of the…

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Q: Ind in =) will it take to reach the ground? [Hint: Find then the height equals zero.] (Round your…

A: Topic:- application of derivatives

Q: Let f(x) = x³ (x + 2)² (x − 3)(x + 4)². Decide whether f(x) is positive on each of the following…

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Q: Can we apply L'Hôpital's Rule for: lim O a. Yes O b. TBH, I don't know. O c. No O d. Maybe. x -?…

A: let  I=limx→0(x4e4x)we know  e0=1

Q: Use logarithmic differentiation to find the derivative of xsinxe2x+3 cos² x y =

A: Topic:application of derivatives

Q: 2- Sketch T and Evaluate the Integral M, divÑav, being ♬(x,y,z) = yĩ+ xyj – zk Where T is the region…

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Q: Let f be defined as follows: x²-9 f(x) = x-3 k if x # 3 if x = 3 What value of k would make the…

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Q: A. Find all the partial derivatives of f(x,y) = 12x²y + 2xy + 5y²

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