Find the value of the following definite integrals. Show your solution. L₂(x¹+4) dx 2. (cos x + tan x) dx 3. (x²+2x+1)dx

Q: sinhr²-² 2 1. lim r+0 sinhr−r

A: To evaluate: limx→0 sinh⁡x2−x2sinh⁡x−x Given limit is of 00 form L'Hospital's rule tells us that if…

Q: Perform the integration. (sinh x)(coth x +csch3x) dx +

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Q: Suppose the ball is dropped at rest from the top of the house 64 ft above the ground and the only…

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Q: Evaluate the integral: 1 - coth² (log₂ x) S² x cosh(log₂ x) dx

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Q: I. Evaluate the following limits. 2. lim (x - Inx)* +0+x

A: We have to find the limit of the function  limx→0+x-lnxx. We can write,    u= elnu Therefore,…

Q: Find the area of the region bounded by the curves y = the x-axis using vertical strip. (x+1)2/ = 4…

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Q: Find the volume of the colld_generated by. revolving the area bounded by the given curves_ about the…

A: We need to find volume.

Q: 3. Find the area of the region bounded by y=x²-2x +2 and y=6-x².

A: Use area under curve

Q: P 1. (1 Use the cylindrical shell method to find the volume of the solid obtained by rotating the…

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Q: Evaluate the limits using the L'Hopital's Rule. lim (tan x) (sin x-1) x+2+

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Q: Solve the differential equation of order one.  (x4 + 2y)dx - xdy=0 STEPS: a. Put the equation in…

A: Separate the equation to form standard form then solve

Q: What is the the x-axis and the semicircle y = (4 - x^2)^1/2? 00 O 1 02 04 ONA x-coordinate of the…

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Q: 3 2 พ 2 cos2 4x dx

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Q: y-coordinate of the centroid of the plane region bounde 22 What is the y = 2x + 1, x + y = 7, and x…

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Q: Find the absolute extremum values of f(x) = xe² xez-2x² 3 on the interval [0, 1]. (Note: ez ≈ 0.22)

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Q: * (sin(2a) + cos(2x)) da Jo

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Q: A group of management students are creating a business plan for their proposed shoe brand Sole…

A: Marginal profit is the profit earned by a firm or individual when one additional or marginal unit is…

Q: Find the area bounded by y = 2x² and y = x a. 9/2 b. 7/2 c. 5/2 d. 3/2 e. NONE OF THE ABOVE

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Q: Sketch the graph of y = x-2 (x+3)²

A: The horizontal asymptotes by comparing the degrees of the numerator and denominator. Vertical…

Q: Using dA = dx dy, set-up the double integral that will find the volume of a solid bounded by z = 1…

A: We need to setup integral.

Q: Determine whether the series 1/4 O 1/2 3/4 + Ex=1 ( 2² - 2 +²+1) 2k+1 0 1 converges and if so, find…

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Q: x-1 x² + 5x + 8 S dx

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Q: Perform the integration. (sinh x)(coth→ x + csch3x) dx

A: A detailed solution is given below.

Q: Use cylindrical shells to find the volume of the solid generated when the region enclosed by the…

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Q: What is the y=x^2 4 and O 1/4 01/2 1 3/2 Ο ΝΑ x-coordinate of the centroid of the plane region…

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Q: P= tan (x- P 1+p²

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Q: The function defined by y=√-² has as its graph a semicircle of radius r with center at (0.0) (as…

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Q: A solid consists of a right-circular cylinder and a hemisphere on each end. The length of the…

A: The diagram of the cylinder with hemisphere on the end will be as following To find dVdr at r=2,…

Q: 2. S 2x 2 5+2x+x -dx

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Q: 2 cos xsinx V2+cosx 1. S- -dx

A: Given

Q: Use the First Derivative Test to find any relative extrema of the function. (a) g(x) = 2x³ – 18x

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Q: Find the Integrating Factor (I.F) of the following linear differential equation: (1 + ²) + y = t…

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Q: What is the center of gravity of the solid formed when the plane region bounded by y^2 = 4x in the…

A: First we sketch the given region using a graphing calculator as shown below:   The shaded region…

Q: Test for exactness then solve. (1 +  y2)dx + (x2y + y)dy = 0

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Q: 0 sinx + 2cosx dx

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Q: ab c Pq r U V W a. det (2B¹) where B = 4u 2a 4v 2b -q 4w 2c <-r 2p -a+u 3u b. det (20¹) where C =…

A: Given problem:-

Q: Find the area bounded by the curve y = coshx and the x- axis from x = 0 to x = 1. a. 11.75 sq. units…

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Q: A rock thrown vertically upward at a velocity of 24 m/sec reaches a height of s(t) = 24t - 0.8t²…

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Q: For several weeks, MMDA has been recording the speed of freeway traffic in EDSA. The data suggest…

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Q: 1. a2 = 6 and a6 = 96 are terms of a geometric sequence, find a4.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Evaluate the following integrals S- 3 • │e* − e| + (e* + = e) + e) dx e 0

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Q: The choice of u and du is subject to trial and error. Identify the appropriate choice of u and dv f…

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Q: V. A small business determined that the price-demand and cost functions for producing and selling x…

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Q: Find the area bounded by the curve 2x² + 4x + y - 0 and the line y+x=0 a. 1.000 b. 1.125 c. 1.525 d.…

A: First we draw the graph,

Q: y s 5 4 -2 -2 The diagram shows the shaded region bounded by the curves y = x² + 2, y = 4 - x, y = x…

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Q: What is the center of gravity of the solid formed when the plane region bounded by y = x^2 and y=x+2…

A: We sketch the given region using a graphing calculator as shown below:   The shaded region is…

Q: 4. Let f(x)= a(7-a2) for all a 0 (a) Find, in terms of a, the equations of the lines tangent to…

A: Given.

Q: Evaluate the integral: 3 So |2 - 2x| dx

A: Given,∫032-2xdx

Q: find the area the of region i) sketch the area, ii) Determine the boundaries ii) retup the definite…

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Q: The equation of a tangent line at a point (x₁, f (x₁)) where limh→0 f(x₁+h)-f(x₁) h = +∞ is x = x1.…

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