Consider the parabola y = 7x - x². (a) Find the slope of the tangent line to the parabola at the point (1,6). (b) Find an equation of the tangent line in part (a). y =

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Q: Find the curl of the vector field F. F=x²yzi+xy²zj+xyz³k curl F = Di+Dj+ Ok

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Q: Find the derivative the function f by using the rules of derivatives. 5x½ 4 a. f(x) = fƒ'(x) = b. f…

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Q: 2- Find the following limits: c) lim x ln (x) x→0+

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Q: Given the function f(x) = -7x - 7, find the total area between f(x) and the x-axis over the interval…

A: Given the function , to find the total area between  and the -axis over the interval .

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A: we have function

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A: we have given surface area of the rectangular solid is 316.5 cm2

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A: we have given velocity function

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Q: -5 100- 5 5.0 10 Here is a graph and an equation that one of your classmates made on Scree 8: y =…

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Q: Consider the function f(x) = 2√x+10 on the interval [4, 7]. Find the average or mean slope of the…

A: Consider the function  on the interval . To find the average or mean slope of the function on this…

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A: The solution is shown in step-2

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Q: 4. For each sequence, prove it converges or diverges. If it converges, find its limit. (c) an (2)¹/n…

A: The given sequence are; c) an=(n/2)1/nd) an= n1/2nFind the sequence is converges or diverges.

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Q: Find the particular antiderivative that satisfies the following conditions: F(x) = F'(x) = x³ +5√√x;…

A: Given:We are required to find:

Q: Find the equation of a plane passing through the points (1,1,-1), (2, -1,4), (-4,1,1).

A: Given three points(1, 1, -1), (2, -1, 4) & (-4, 1, 1)

Q: Find and classify (using the second derivative test) the critical points of the function f (x, y) =…

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Q: Determine whether the lines L₁: x and :x= 19+ 6t, y = 18 + 6t, L₂x = -13 +7t y=-16 + 8t z = -22 +…

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Q: Find the demand function x = f(p) that satisfies the initial conditions. 600 (0.02p - 1)3' dx dp x=…

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Q: If y y= -5 csc (5-6x2), dy dx = find dy dx

A: IfFormula Used :

Q: Find the area bounded by the curve x² = -y and the line y + 4 =

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Q: MUINGWEVER Use double integrals to compute the area of the region bounded by y = 7+7 sin x and y=7-7…

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Q: Use L'Hospital's rule to find the limit. (a) lim x-1 x²-3x + 2 x² - 1 sin (2x) 2-0 sin (7x) (b) lim

A: L'Hospital's rule a.

Q: Determine all the points where the given function is continuous f(x,y,z)= x² + sinz y a. All of R³…

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Q: dP = The population of a town is growing at a rate given by 78 - 6t people per year. Find a function…

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A: The solution is shown in step-2

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Q: 31. ₁*√ (1 + 1) dt St √√t t) 33. T/4 1 + cos²0 cos²0 ST7/4 ӨР 32. /sece tane de

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Q: Which of the following is the special solution of the equation y" - y = 3x + 2 using the operator…

A: The given equation is; y''-y=3x+2

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Q: 7. Prove by definition that limx→1 x³ = 1. [Hint: x³ - 1 = (x − 1)(x² + x + 1).]

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Q: 1-2 -2)(3-2) 9(0) 0 47

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Q: Use the figure to answer the questions. B y X (a) At each labeled point on the graph, identify…

A: Instantaneous rate of change is given by the slope of tangent at that point on the curve.

Q: 4dx x3-4x²+8x

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Q: The average cost of a product changes at the rate C '(x) = −8x−2 + 1/8 and the average cost of 8…

A: Given that, the average cost of a product changes at the rate of  and the average cost of the 8…

Q: 10. ²x+6 (Partial Fractions) (Ans: 2 In x- - - in |x + 3| - arctan () + C) 3 x + 3x

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Q: 1. Find an equation of the plane tangent to the surface x² + y +z = 3 at the points (1,1,1) &…

A: Equation of tangent plane :- x² + y + z = 3Points:- (1, 1, 1) & (2, 0, -1)

Q: Evaluate the integral with new limits of integration. (Use symbolic notation and fractions where…

A: Given that a integration and we solve this integration by using the general property of integral.

Q: Use cylindrical coordinates. Evaluate III. x2 dv, where E is the solid that lies within the cylinder…

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Q: Find the absolute maximum and minimum of f(x, y) = 5x + 2y within the domain x² + y² ≤ 3². 1.…

A: We need to find the absolute minimum and maximum of within the domain

Q: Find the Maclaurin series for f (x) using the definition of the Maclaurin series. f(x)=xcos(5x) O a.…

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Q: Refer to the figure. U₁ = ||v||. V U₂ = ||v||. 30° u 45° 15⁰ q 20° Find the components of v. (Use…

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Q: For the vector-valued function r(t) = (cos 2t, sin -(cos 2t, sin-4) 3 (4) what is the magnitude of…

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Q: Use the information about values of the functions and their derivatives to calculate H'(3), where…

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Q: h(x, y, z) u = i + 2j + 2k cos xy + e + In zx, Po(1, 0, 1/2),

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Q: Find the second derivative, d^2y / dx^2, where y is defined as a function of x implicitly by the…

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Q: Solve the given differential equation by using the superposition approach. y" - 2y' +17y=e* cos(4x)

A: The given differential equation is of type, Therefore, it is a non-homogeneous differential…

Q: Solve the given initial-value problem. y(x) = y" + 4y + 4y = (7 + x)e-2x, y(0) = 6, y'(0) = 9 -2x₂…

A: By finding complementary function and particular integral, we can solve the initial value problem.

Q: The following graph shows the number of housing starts for sale purposes in the United States during…

A: The following graph shows the number of housing starts for sale purposes in the United States during…