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Q: 2-4х3 3. lim х--0- 5x2+3x3

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Q: M3.2 Trigonometric Groups 3. S sin³x cos xdx 4. S Vtan x sec*x dx

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Q: A) If (xn) is a decreasing and bounded sequence. Prove that (xn) is convergent with lim Xn inf {xn :…

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Q: 2. S(r2 +r + 1)e"dr 3. Find the area of the region in th

A: Given problem:- ∫ (r2+r+1)er dr

Q: 0. 21XVX2 + 1 dx = 142 7, what is | 21uVu? + 1 du? Given that %3D 1

A: here just we put x =u so deside the function is odd or even so lets put u = -u 21(-u)(-u)2+1…

Q: 7458 B2 Follow the solution format on the picture.

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Q: Solve the exponential equation by using the property that b^x= b^y implies x=y, for b>0 and b≠1.…

A: Given query is to find the value of x.

Q: 1 (5* )csch- if y= (e oshS ) In Vx² +1 2 a) Find dx dy x+1 x>0. 2 x++1

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Q: In dx

A: Given: I=∫lnxx2dx   As we know the Power rule: ∫xndx=xn+1n+1+C

Q: Find the integral of: * |x In(x + 1)dx 1 1 1 * In\x + 1| +x² +x+;In |x + 1| + € 5x² Inlx +…

A: Here we have to do integration by parts.

Q: Find an equation of the plane through (0, –9, –1) that is perpendicular to the line x – 2 = 3t, y +…

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Q: :- Solve the following two equations by applying the idea of Gauss-Siedel iteration. -+2y-5%=0, 4…

A: Let's find.

Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: We need to find directional derivative.

Q: Y2 = Find the area bounded by these curves. (All choices are in sq. units) Y1 = Vx + 3 (x+3) Y2 = 2

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Q: In the figure, a 2400 kg demolition ball swings from the end of a crane. The length of the swinging…

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Q: Show that the lines L1 : x = 4 – t, y= 2t, z = 5+t and L2 : x = 1+4t, y= 3 – 8t, z= 5 – 4t are…

A: Let's find.

Q: Find dx (9x² + 16 1 1 - In |3x + V16 + 9x²| + c -In |3x – V16 + 9x²| + c Option 2 Option 3 1 1 In…

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Q: What is the length of a simple pendulum whose full swing from left to right and then back again…

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Q: Eind the area of the given region. Use a graphing utility to verify your result. (Round your answer…

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Q: Given .5 8 | f(=)dz = /f(2)dz + f(2)da – | f(a)da, -6 6 what are the limits of integration a and b?…

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Q: 7. Approximate (22 + 3) dz using four rectangles and the left endpoint method.

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Q: Find the area bounded by these curves. (All choices are in sq. units) y = x 4x +y = 12

A: Here, the is a line passing through the origin. And,  4x+y2=12⇒4x=-y2+12⇒x=-14(y-0)2+3 which is a…

Q: (6) At the start, an experiment records 1 gram of bacterial culture, and the culture's weight is…

A: Given: The initial amount of bacteria i.e. at t=0 hours = 1gm The culture's weight carrying capacity…

Q: A rectangle sheet of cardboard measures 16 cm by 6 cm . equal squares are cut out of each corner and…

A: We need to find maximum volume.

Q: In Pi Jinxing's dream, two curves are said to be CoRoNaViRaL if whenever they intersect, the two…

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Q: The line through (8, 5) that is parallel to 3i+2j. Ox = 8+51, y = 3+2t Ox = 8+81, y = 5+5t Ox =…

A: Given query is to find the equation of the line.

Q: Perpendicular to the plane z + 3y – x = 7 and containing the points (2, 5, 0) and (0, 2, -1)

A: Solution of question is written in below steps.

Q: /9-y dy

A: We have to integrate.

Q: 9. Write as a single integral in the form f(x) dx. -1 f(x) dx + f(x) dx - f(x) dx -4 f(x) dx

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Q: Find an equation of the plane through (0, –9, –1) that is perpendicular to the line x – 2 = 3t, y+3…

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Q: АCTIVITY GIVEN : 2x 2x 1 2х + 3 1 f (x) = 1 –x 8 g(x) = 3(x + + 4 h(x) = 6 a.lim -4 · f (x) d.lim (8…

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Q: Identify the open intervals where the function is changing as requested. Increasing 3 45 6 O (-3,…

A: Increasing

Q: Given the function f(x) = (÷) (a) Find a power-series representation for f(x). Σ п(п +1) (п + 2)!…

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Q: Use integration by substitution and the Fundamental Theorem to evaluate the definite integral. NOTE:…

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Q: Solve the attached integral problem

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Q: 3. According to Newton's cooling law, the rate of cooling of a hot body is pro- portional to the…

A: According to Newton's law of cooling, we have T(t)=Ts+(T0-Ts)e-ktwhere T(t)- temperature of body at…

Q: In(5x2 + 8) Find the slope of f (x) at (7, 1.84). Use a graphing utility and round to the nearest…

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Q: The graph of a function f(x) is shown below. If the definite integral | f(2)dz gives the area of the…

A: Given query is to find the area under the curve.

Q: Find the x-coordinate of the inflection point(s) of y = f(x)

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Q: S 4x cos(2 – 3x) dx

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Q: Consider the following. u = -9i - 2j - 4k, v = 4j + 4k (a) Find the projection of u onto v. -3j – 3k…

A: The given vectors,u=-9i-2j-4k, v=4j+4k

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (– 10,…

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Q: 1 (5* )csch dy x+1 1. (а) if Find dx x > 0. y = (ecosh S* ) In(Vx² +1

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Q: (a) Oppositely directed to v = (3, -4) and half the length of v. %3D W3= (?, ?) (b) Length V5 and…

A: To Find : a) A vector which is oppositely directed to v=<3,-4> and half the length of vb) A…

Q: dy +y = y² sin x dx

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Q: d (cosh* 3x– sinh* 3x)= In(x + Vx² -1). -1 (b) Show that for x 2 1, coshx- - dr

A: This is a problem of trigonometric hyperbolic inverse identity. Based on the fundamental formula we…

Q: (29.4) Determine whether the series (-1)"-1. n2 + 1 is absolutely convergent, condi- n=1 tionally…

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Q: Match the answers to its antiderivative. Antiderivative Answer A. J kda In(z) + C II. B. ['dr + C…

A: As we know that; The Power rule; ∫ax+bndx=ax+bn+1an+1+C ; n≠-1 And ∫eax+bdx=1aeax+b+C…

Q: 10 40 What does that mean 11 Suppose f(x)dx : f(x)dx is equal to? 10

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Q: State the answer using combinations. c) The number of edges in the complete graph K21. d) How many 7…

A: We will answer only part c, d and e because you have mentioned to solve only these three.   Complete…