Evaluate the limit using L'Hôpital's rule 7x³ e10x lim x →∞

Q: 10. Find a formula for the function f(x), given the information that f is continuous and th f(t) +…

A: Given that f is continuous and 4x+∫1xfttdt=sin x. We have to find the formula for fx.

Q: Convert the Cartesian coordinate (-1,-5) to polar coordinates, 0≤ 0 < 2π

A: Given,            The cartesian coordinate is -1,-5.To find : Convert the given cartesian coordinate…

Q: Question 22 Find the average value of f(x) = 8x - 4 from 1 to 5. The average value of f(x) = 8x -…

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Q: For the equation given below, evaluate y' at the point (2, –1). y'at (2, -1) = e³ + 10 − e¯¹ = 2x² +…

A: To find derivative of the given function.

Q: . Let ƒ(x) = (x² - 4)³. Do the following. (a) Find the maximum value and the minimum value of f on…

A: We have to solve given Questions.

Q: Step 4 We have a general solution to our differential equation: y = ₂0.08t + C - 25,000. To find the…

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Q: Given vectors u = (-33, 6) and v = (-19,5), find vector u — v.

A: To find the vector difference

Q: Question 23 Find the area between the curve f(x) = x^2+15 and the x-axis from x = 2 to x = 6. the…

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Q: Let A be the area of a circle with radius r. If dr dA dt when r = 5. dt = 3, find

A: Given A = Area of the circle r = radius of the circle drdt = 3 r = 5 dAdt = ?

Q: Draw a sketch of the region d. Find the area of the region e. Find the volume of the solid generated…

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Q: At what interval is y=2x4-4x2 decreasing?

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Q: Given vectors u = (7,-4) and v = (-8, -7), find u v.

A: The given vectors u=7, -4 and v=-8, -7. We have to find the value of u·v.

Q: Find the average value of the function f(x, y) over the plane region R. (Give your answer correct to…

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Q: question 30 Find the area enclosed by the curves f(x) = 37 - x^2 and g(x) = x^2 The area (rounded…

A: Given functions fx=37-x2,gx=x2

Q: Find the area of the shaded region. 28) (0,0) y = x³ - 4x 3 (3,15) %

A: Consider the figure given below :

Q: Find the area of the region bounded by the curves x = 2y ^ 2 and x = 4 + y ^ 2 Be sure to justify…

A: We have to find the area enclosed by the curves using integration.

Q: (a) 2 P₁² (20- 1 (x-1)e(x-1)² dx

A: We have to solve this definite integral  Which can be solve by using substitution method.

Q: Particle P moves along the y-axis so that its position at time t is given by y(t) = 4t² - 5t + 7 for…

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Q: Given f(x, y) = sin(x + y) where x = : s¹tº, y = 4s – 6t. Find f(x(s, t), y(s, t)) = ft(x(s, t),…

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Q: Use the Ratio Test to determine whether the series convergent or divergent. Identify an n = 1 n! n…

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Q: Consider the following. = 3x³ + x y = (a) Find the interval(s) of increase. O (-∞0, 0) 0 (0,00) O…

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Q: Write an equation describing the relationship of the given variables. y varies inversely as the cube…

A: Given that y varies inversely as the cube root of x.

Q: Find the slope of the line tangent to the following polar curves at the given points.

A: According to question,Given Polar curve,r2 = 4 cos 2θ

Q: Evaluate (2xy³ − y² cosx) dx + (1 – 2ysinx + 3x²y² )dy y² from (0,0) to (ñ/2, 1) along the parabola…

A: According to question,Given Integral,∫c2xy3-y2 cos x dx + 1-2y sin x + 3x2y2 dy

Q: f(x)= x^2log(x) look at the graph to find which function dominate the polynominal or the logarithm.…

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Q: Find the area inside one leaf of the rose: r = 5 sin (30) The area is

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Q: 12) y = 2-X ; 3x+1 A) -7 (3x+)² B) dy = ? 6x-5 (3 XH)² (3x+1) DJ 3+2x

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Q: [xln x In √x dx

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Q: Solve for t:   7e-.045t=15

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Q: Find the integral of F(x) = √ 2x + 3 over [-1, 1], using Riemann sums with n=4 and the midpoint of…

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Q: The radius of a circular oil slick expands at a rate of 6 m/min. a) How fast is the area of the oil…

A: Given is to find the rate of change of area

Q: Solve for y:  3log10(y)=-6

A: NOTE: Refresh your page if you can't see any equations. . divide both sides by 3

Q: Given the following vectors, calculate 5u + 3v. |(7, 0), v = (-8, 10)

A: We need to perform the given algebraic operations on the vectors. The detailed solutions are…

Q: 2- Find the equation of the tangent line to the curve 9xCos(7y) + 5y = 9 at y = 0.

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Q: Find the equation of the parabola described below. Find the two points that define the latus rectum,…

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Q: Calculate the slope of the tangent to the curve of the following formulas: y = -x + 6x + (x + 9)² at…

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Q: A forest fire is found at midnight. It covers 1100 acres then. It is spreading at a rate of f(t) =…

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Q: You want a linearization that will rep subsequent work as simple as possib which the function and…

A: Take x = a = 4

Q: Ordinary Differential Equations of the First Order.pdf Exercises: 1. y(2x-y+1) dx + x(3x-4y+3) dy =…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 2- Find the equation of the tangent line to the curve 9xCos(7y) + 5y = 9 at y = 0.

A: To find the equation of the tangent line to the curve 9x cos7y+5y=9 at y=0.

Q: 8. √(T-2) 0 - x) сos лx dx

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Q: Evaluate the definite integral 7 S₂ (8x + 2)dx

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Q: 6- Find the volume of a solid, use the Cylindrical Shells method, which involves rotating the region…

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Q: Determine an equation for the level surface of g that would pass through the pointa: (-7, -2, 5).…

A: We need to find level surface.

Q: 4 Find the equation of each graph after the given transformation. a y = 3x² after a stretch parallel…

A: Let's find equation of each graph after the given transformation.

Q: Suppose f(x, y) = 5y - 9x Find an equation for the level curve of f that passes through the point…

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Q: If f(x) = sin(x³), find f'(x) Find f'(5)

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Q: Evaluate the integral √² (²2/1 + ²)² = 24 dr= 24 7 dr.

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Q: The angle addition formula for cosine is cos(a ± ß) sin a sin ß. Use this formula to find the exact…

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Q: Find the area of the shaded region. 30) f(x) = -x3 + x² + 16x g(x) = 4x -4 (-3,-12) -2 30- 20- 10…

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