Definite Integral and Plane Areas by integration (snow solution) dx + So - 2 1+x 2. S dx 25-x2 = 1/2 in 13/1/20 In

Q: 60. (a) dx SI dt 1 + √t (b) de fint di dt

A: We can solve this as follows:

Q: 1 xVx+3 xp:

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Q: Problem 4 The helix r(t) = (cos(xt/2), sin(xt/2), t) intersects the sphere x2 + y² + z² = 2 in two…

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Q: Find the volume of the solid obtained by rotating about the y-axis the region bounded by y = 2x² -…

A: Solution of given question is written in below steps.

Q: Sπ/4 x² dx (x²+4)5/2 (Use trigonometric substitution)

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Q: Question 2 Consider using the method of partial fractions to solve rb dx = Sa 2x²+2+x³+x² dx = [Aƒ…

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Q: what is the normal equation to the curve which is the circle with center at origin and and radius of…

A: Given circle , With center at origin (0,0) And a point on circle is (4,3)

Q: 19. -π/2 21. -π/4 23. [³5e* dx sin 0 de cos x dx sec² 0 do (2x secx tan x) dx 20. rπ/3 22. 24. [¹-dx

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Q: Determine the interval(s) on which the vector-valued function is continuous. (Enter your answer…

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Q: Describe the graph of the equation. r = (4 - 3t)i - 7tj O It is a plane in 2-space that goes through…

A: Given equationr=(4-3t)i-7tj

Q: 7. lim y→∞ y² – е6 y 4y² + e7y

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Q: Find T(t) and N(t) at the given point. T(0)=(1,1,1) N(0) = (0, 2, 1) x = e cost, y = et sint, z=e¹;…

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Q: Consider using the method of partial fractions to solve x²+x+1 Sa 2x²+2+x²+x A In(x²+1) B x+2 D…

A: This is a problem related to integration of the function using partial fraction decomposition. Based…

Q: ♫♫¹⁄² sin (*) cos (*) sin (²) dx (Consider initially the first 2 terms)

A: Solving the definite integral.

Q: Identify the surface that corresponds to the equation 3y^2 - 2x - 8z^2 = 0. O elliptic hyperboloid…

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Q: ... : S (1 + 2x) e-x dx. Using integration by parts and letting u = -1- 2x, dv = 2 f(x)dx, then the…

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Q: Given: (1+2x) e-x dx. Using integration by parts and letting u = -1- 2x, dv = f(x)dx, then the value…

A: Let's find.

Q: √x²-9 √ di Using trigonometric substitution, what is f - dx ? x3

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Q: sec+2x tan 2x and -dx 11 1 I + 12 tan 2x 16 tan³2x Ⓡ (cor³2x) ( 1+3csc22x 12 Ⓒ/cot²2xcot³21+C 16…

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Q: V. Given: 2. Find f'(2), if it exists. el3z-61-2, f(x)=[2x - 5], √x²-9, if x ≤2 if 2 3

A: Solution is given below:

Q: Explain why you think the sequence 1-(-1)" con converges to a finite number or n+1 diverges. If the…

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Q: el3-6-2, if x ≤2 if 2 3 Find f'(2), if it exists.

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Q: Let T: R³ → R³ be a linear transformation such that T(1, 0, 0) = (4, -1, 2), 7(0, 1, 0) = (1, 3,…

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

Q: 62. du * |x|dx

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Q: Question 12 Determine the equation of the vertical asymptote and the equation of the slant…

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Q: 1. ) cos (4) COS -π/2 f/² sin (1) sin (²) dx (Consider initially the first 2 terms)

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Q: (D² – D − 2)y = cos x

A: Here is the solution:

Q: Find all real solutions of the equation 2g² = 50. Write your answers as a list, using a comma to…

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Q: dy/dx of sec^2 (x^pi - pi^y)

A: To find the derivative of given function.

Q: Sa 2x²+2+x³+x² =dx = [Aƒ (x) — B ln(g(x)] + D fb dx, and if A = ,B<0, then f(x) dx x+2 x² 2x + + 5…

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Q: Use linear approximation or differentials (but not both) to estimate: cube root of 7.98 Is your…

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

Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 3. lim (x-3) tan(9-x²)…

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = 3t³i + 6tj - t²k (a) r(t) (b) r"(t) (c)…

A: Given data÷

Q: Consider the quadratic function f(z) - 2² +0z + 4. Determine the following: (enter all numerical…

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Q: 20. To solve S for this integral? A(2x) + B x² A. B. C. 22-12x dx, partial fraction is to be…

A: The given integral,      ∫22-12xx23x2-10x-8dx

Q: 1. ² sin() cos() sin(x) dx (Consider initially the first 2 terms)

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Q: Let (A) = and B = . Find the angle between BO and A D O 【cos) 2/√(30(21)) O [cos] ^(-1) 2/√(30(21))…

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Q: Explain why you think the sequence converges to a finite number or (n+1)! diverges. If the sequence…

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Q: 20 x³ dx (x²+4)5/2 (Use trigonometric substitution)

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Q: Find all real solutions of the equation 8m² -18-374. Write your answers as a list, using a comma to…

A: A detailed solution is given below

Q: Find F'(x). 1. F(x) = √x+² (4t + 1)dt 2. F(x) = f*t³dt SOLUTION IN HANDWRITTEN

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Q: Determine the open intervals on which the graph of = 3x² +7x - 2 is concave up or concave down.…

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Q: Question 10 > Put a dot on the vertex of the parabola below. What is the coordinates of the vertex?…

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Q: Determine the order of the given differential equation and state whether the equation is linear or…

A: Here we have to determine the order of the given differential equation and state whether the…

Q: 4. Evaluate the following sin(x)cos(2x)sin(3x) dx sin(3x)cos(3x) sin(2x)cos(2x) 12 sin(2x) sin(2x)…

A: Solution: ∫sinxcos2xsin3xdx

Q: Question 16 A line through (-1, -2) with a slope of -10 has a y-intercept at

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Q: -π/4 x3 dx (x²+4)5/2 (Use trigonometric substitution)

A: We have to solve above question useing trigonometry substitution

Q: Find an equation of the plane containing the point (3,0.-4) and perpendicular to the line r(t)=…

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Q: Question 7 10 -8 -6 -4 -2 8 10 -2- -4 -6 -8 -10 Write an equation for the graph, where y depends on…

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