10. Find the indefinite integral J dx (3+5)2 dx

Q: If g(x)=√1+tdt, then find the derivative g'(x).

A: Given :- gx=∫0sinx1+tdt

Q: What is the vertical asymptote for the function f(x) = 1 4x Ⓒx=0 x = 1 x=4 y=1 ? 61

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Q: 1. Let f: R→ R such that f(x) = -x ifa is rational and f(x) = 2x+3 if x is irrational. Prove that f…

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Q: Consider the following graph of the second derivative, f" (x), for some function f (x): f"(x) 9- 6-…

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Q: Problem #2: Evaluate the following integral, £xx² ds where C' is given by y = x¹0 for 0 < x < 1.…

A: Given integral is ∫Cyx7ds, where C is given by y=x10 for 0&lt;x&lt;1

Q: Find y" by implicit differentiation. x² +9y² = 9 y" =

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Q: d) find the displacement (change in position) between 1 and 3 e) find the average velocity (rate of…

A: According to question,Given Position function,x = 8 sin πt6

Q: roasted turkey is taken from an oven when its temperature has reached 185 Fahrenheit and is placed…

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Q: Find f(x) if f"(?) = 12x^2+6x−4 and f(0) = 4 and f(2) = 10

A: f''(x)=12x2+6x-4f(0)=4f(2)=10∫xndx=xn+1n+1+c

Q: For each function, use our techniques to sketch the graph. Include asymptotes, at least one…

A: (a) Given that,              y=xx-1 x-intercept:            y=0 ⇒xx-1 = 0           ⇒x=0…

Q: An initial investment amount P, an annual interest rate r, and a time t are given. Find the future…

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Q: 2. xy=-x³y-csc (xy)

A: Given differential equation:- x4y'=-x3y-cscxy

Q: Find the extreme values of f subject to both constraints. (If an answer does not exist, enter DNE.)…

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Q: Throughout this problem, consider R to be the region between the curves f(x) = 2x and g(x) = x³ in…

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Q: On which interval f(x) = -2³ + 3x² - 4 is concave upward? O a. (-1,1) O b. 1 Od. >1

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Q: Find the volume V of the solid obtained by rotating the region bounded by the curves y = 6/x, x = 1,…

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Q: Integrate the following function with respect to x using partial fraction 2x - 3 r2 – 52 +6 and…

A: Given: ∫012x-3x2-5x+6dx

Q: Let the function f(x) have the property that f'(x) g'(x) = = = x+5 x-2 ¸ If g(x) = f(x²) find g'(x).

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Q: find the volume of the solid revolution generated by revolving the region bounded by y=e^(3x) y=3…

A: Given curves equations:- y=e3x,y=3,x=0

Q: The so-called cuspidal cubic is given parametrically by the equations x = t³, y = t² Compute the arc…

A: It is given that x=t3y=t2

Q: Suppose that 336 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: Length of rectangle=x ft Width of rectangle=y ft Radius of semicircle r=x2ft

Q: b. Use the substitution x = u² and the fact that S e-u² du VI = ¹(²-) = √². to show that I

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Q: Find the directional derivative of the function at P in the direction of v. g(x, y) = √√√√x² + y²₁…

A: Given query is to find direction derivative.

Q: Solve the following linear programming problem. Restrict x ≥ 0 and y ≥ 0. Maximize f = 7x + 9y…

A: Given : Maximize f = 7x+9y subject to constraints 2x + 4y ≥ 8 ⇒   x + 2y ≥ 4 3x + y ≤ 7 y ≤ 4   Plot…

Q: 15. Evaluate the limit for the graph: lim f(x). *→2* 4 +∞o a. b. -1 14 A 2 -2 0 2 A C. d. 2 does not…

A: Solution:

Q: The position function of a particle is given by r(t)=At what time is the speed minimum?

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Q: Set up iterated integrals for both orders of integration. Then evaluate the double integral using…

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Q: Solve the given differential equation. dy + In xy dx = (10x + In y)dx y=0

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Q: Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 1. Given that y² = 48sin 0 and dy/dt = -5, find de/dt when 0 = TT/6

A: Given y2 = 48sin(thita) dy/dt = -5 thita = pi/6

Q: Some airlines have restrictions on the size of items of luggage that passengers are allowed to take…

A: Let the length , width and height if the luggage is l , w and h.

Q: Find f'(x) and find the value(s) of x where the tangent line is horizontal. f(x) = x²(x-12)5 f'(x) =…

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Q: As the wheel of radius r cm in the figure rotates, the rod of length L attached to point P drives a…

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Q: Find the profit function if cost and revenue are given by C(x)= 150 +3.7x and R(x)= 3x -0.06x²

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Q: 3. Let f(x,y)=x²y/(x² + y²). (a) Show that f(x,y) goes to zero if (x,y) goes to (0,0) along any…

A: Solution: (a) If (x,y) approaches (0,0) along the straight line y = mx, then we can substitute mx…

Q: Find the distance between the skew lines r(t) = (5, 0, – 3)t + (− 8, 7, - 2) and p(s) =(2, 1, 4)s +…

A: I have done solution step by step in detail...go through the solution

Q: Solve the given differential equation. 7ydx - 7xdy+x+dx=3dx The solution is 0. (Type an equation.)

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Q: Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

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Q: What is the relative minimum value of the function f(x) = 5-6x - x²? Of(x) has a relative maximum…

A: Since you have asked multiple questions, As per the guidelines we have to solve the first question.…

Q: A fluid moves through a tube of length 1 meter and radius r = 0.004±0.00025 meters under a pressure…

A: Given that r=0.004, ∂η∂r=0.00025, p=2×105, ∂η∂p=1000v=0.875×10-9, ∂η∂v=0And η=π8pr4v

Q: lim x-1 d x3+5 xa - X-5 * ха x2 + 4x -5

A: According to question,Given limit,limx→1 x3+5x2-x-5x2+4x-5

Q: Fully factor and find all of the specific zeros of the function f(x)=2x4-9x³ + 6x² - 9x +4 Show your…

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Q: Find the angle of inclination of the tangent plane to the surface at the given point. x² + y2 0 = =…

A: Given query is to find indicated angle.

Q: Find f. f(t): = 12t f"(t) = 3 9 √t' f(4) = 32, - 22t + 6 X f'(4) = 14

A: f''(t)=9tgiven  f(4)=32f'(4)=14∫xndx=xn+1n+1+c

Q: The diagram above shows the graphs of y = e-* (red) and y = x (blue). (a) State the equation in x…

A: Point of intersection refers to the point where the graphs intersect. Graph is a diagrammatic…

Q: (b) (c) Ο Ο Ο Ο 0 Ο Ο Ο Ο 8+6=2 8 2 = 6 2+6=8 8 6 = 2 ( 6 + 2 = 8 L 8 1 8+6=2 +1 8 0 1 2 3 4 5 6 7 8…

A: To solve the following problem

Q: Find (without using a calculator) the absolute extreme values of the function on the given interval.…

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Q: Let D be the region bounded by the graph of y = 1 - x4, the x-axis and the y-axis in the first…

A: The given data is: y=1-x4x=0y=0

Q: For the formula at the given point, find the equation of the tangent line 5. y=x²e at the point…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…