Q3/Evaluate four of the following integrais dx dx c. fd. sex C. sec²x e. f(3x + 2)5 dx

Q: 0 x cos nx dx X

A: Topic: Definite integral

Q: X=2Seco y = 4 tano find cay dx² 1. when 0-1

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Q: 3 Só ( x + ²/2 ) ²³ dx X

A: integration

Q: 9. (20 pts) Find the area between (bounded) by the curves y = x² + 10x and y=2x+9.

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Q: If f(x) = x'ex, find f'(x) and f'(1).

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Q: b.) Inside r= 3 sin and outside r= 1 + sin &

A: This is a problem related to area calculation of the polar curve. Based on the general formula and…

Q: Find the critical point and the intervals on which the function is increasing or decreasing and…

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Q: The average rate of change of f(x) = sin(x) with respect to x as a changes from 0.5 to 1 is O 1 0 2…

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Q: Compute the divergence and curl of F= -(z³-3x)j+4y²k+x²yi

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Q: 2. Evaluate: 0 √|2 − x + x dx

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Q: of Taylor series for F(x) = Sin(pnx) + ex-p, about

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Q: Get the second and third derivative of function: y'= 3x^2y^2

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Q: 6. Use a change of variables to evaluate | 23e2x4+7 dr.

A: Solution is given below..

Q: etch the region enclosed by y = x²y = √√x,x = 0,x = 1 and find its area.

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Q: 8. Consider an object moving along a line with velocity v(t) = 6t2 - 12t with t measured in seconds…

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Q: A spherical tank of diameter 6 m is full of water. Find the work done in pumping all the content to…

A: Follow the procedure given below.

Q: Q2/Test whether the differential equations are exact and solve those that are. (Answer only two) -y²…

A: We have to solve given differential equation.

Q: 4. Let z = x2 + y³, x = 2st, y = s - t2, s = u", and t = u sin w. Compute for Oz ду and дw ди

A: Let z=x2+y3, x=2st, y=s-t2, s=uw, and t=u sin w.To compute for ∂z∂w and ∂y∂u.

Q: The graph shown is the 1st derivative of function where its domain is R फ़ी An interval where the…

A: topic - strictly  decreasing  interval of function

Q: Y y=√√√1-x² x Show that the volume under the surface z = 5x²y over the half of the unit above the…

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Q: Determine the intervals on which the function is concave up or down and find the points of…

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Q: (-3, 3) & (0, 0) Y₁ = X₁ = ; X₂ = Trend: m = 3 Y₂ = Final answer:

A: Solving the problem by finding the slope and trend.

Q: Find two polar coordinate representations for the rectangular coordinate point (-√2, √6), one with…

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Q: Please fix the mistakes that are in Red for me.

A: Note: Since you have posted a question with multiple subparts we will solve the first three parts…

Q: Obtain the output for t = 1.22, for the differential equation 2y"(t) + 27y(t) = et + et :y(0) = 0,…

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Q: Find the volume of the solid generated by revolving the region bounded by y=3/(2√x), y=0 & 1s XS4.

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Q: Show that f Va²-t²dt = a² sin-¹(2) + x√a²-x².

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Q: dx ylnx dy || y + 1 X 2

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Q: (a) What angle in radians is subtended by an arc 1.50 m long on the circumference of a circle of…

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Q: R 쫘 = 0.138 & R" . R₁ " 0.126

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Q: gh (2,-5), parallel to y= 2x+4

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Q: 6 Consider the three by three system of linear equations 2x + Y + + 2y + 2z 5z 12. We will solve…

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Q: For the F(x) function shown in the figure, find P(0≤x≤0.5) F(x) 1 1 2 1 2 1 X

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Q: (31) Use Newton's Method to make the second approximation x2 to the solution of 2e* = ex. Take x₁ =…

A: We have to use Newton's Method to make the second approximation.

Q: Find (au/ay), at the point (u,v)=(√2,-2), if x=u² + v² and y= uv. du (Simplify your answer.) ay…

A: Here we using jacobian formula.

Q: 3 1 L ₁₂x²²49dx +9 -3 RE

A: We have to find value of given Integral.

Q: Acceleration due to gravity in feet per squared second is the constant function a(t) = -32. Suppose…

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Q: The equation of a hyperbola given below when reduced to standard form is 16y² -9x² +36x +96y - 36 =…

A: solution:-16y2-9x2+36x+96y-36=016y2+96y-9x2-36x-36=0  to make perfect…

Q: 5. √√64 .05

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Q: 4.3√√√7

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Q: 2 4 cot 4 x dx

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Q: Find the instantaneous rate of change for the function at the given value. f(x) = x² + 3x at x = 0…

A: We can find the instantaneous rate of change as below

Q: Find the transition points. y = 15x³ + 360x² (Use symbolic notation and fractions where needed. Give…

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Q: 1. Solve the following equations: c) (x² - 4xy - 2y²) dx + (y² + 4xy - 2x²) dy = 0

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Q: Show that the particular solution of the differential equation d²y dx² -6y-12(x+ e*) +5% dx 5 is…

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Q: Question 2 What is the slope of the tangent line to the graph of x² - xy - 4y² + 2x + 4y = 8 at (4,…

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Q: Find the transition points. f(x)= x(11x) (Use symbolic notation and fractions where needed. Give…

A: Given problem:- Find the transition points.   f(x)= x(11-x)1/3 Find the intervals of…

Q: Find the transition points. y = 3x³ - 45x³ (Use symbolic notation and fractions where needed. Give…

A: We have to solve given Questions.

Q: lim (3x - 5) x--1

A: limx→-1(3x-5) = limx→-13x - limx→-15  [ lim(a - b) = lim a - lim b ]                         = 3…

Q: 2) Find the average value of the function f(x, y) = 6x + 4y over the plane region R. defined by the…

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