I. Evaluate 4x² + 4x + 5 dx

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A: Here we have to apply trigonometric substitution.

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Q: What are the polar coordinates of the point P shown below? 2 3 4

A: This question is related to coordinate systems, we will solve it using given information.

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Q: If you are going to evaluate the x²+16 using trigonometric substitution, the answer is =-csc*Ø + C,…

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Q: Evaluate. Submit your solution in google classroom sec* 2t dt tanº 2t O -1/(12tan^6 2t) - 1/(16…

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Q: |(x² + a) 5 5x The resulting integral of dx is In +eTan-1X + C, where a, b, d, and e are integers.…

A: Given:        ∫5xx3+x2+4x+4dx Apply linearity:     =5∫xx3+x2+4x+4dx Factor the denominator:…

Q: 4. The surface described by the equation x2 + y + z² = 0 is a(an) (a) elliptic paraboloid symmetric…

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Q: Find the points on the ellipse 5x2 + y² = 5 that are farthest away from the point (1, 0). smaller…

A: To find the points on the ellipse 5x2+y2=5, that are farthest away from the point 1, 0.

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Q: usider (x. Using a suitable trigonometric substitution, the resulting integral in terms of 0 is…

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Q: |v|dt. Then find the Find the arc length parameter along the curve from the point where t= 0 by…

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Q: 5x -dx? J x³ + x² + 4x+4 How many quadratic and distinct factors are in the denominator of

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Q: integral

A: We have to choose the correct option from the given options according to the given information

Q: y" + 4y' = cos(t – 3) + 4t, y(3) = 0, y'(3) = 7

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Q: 'n = 1 n (- 1) "xη Σ 'n = 1 n2 8. 8.

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Q: 1. The angles of a quadrilateral are in the ratio 2:4:5:7. Find all the angles.

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Q: 1. Evaluate the following limits. 2 - V2r + 10 a. lim 1-3 x2 + x – 6 4x – 7 lim z+-1- \3x2 – 2r – 5…

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Q: 2x4 + 3x2 – 1 Rewrite dx as integral of sum of partial fractions. (x³ – 4x² + 5x)² C D E F + |dx x2…

A: First we factorise the denominator of the given function.Then write the given integral into integral…

Q: in how many distnct ways can the letters of the word DEEDS be arranged? Oways (Type a whole number)

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Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). r(t) = t’i + t°j 70 t4 K(t) (4 + 49 t10)ž

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Q: Determine the general equation of the plane Ω passing through the point P(1, -4, -5) and parallel to…

A: Given: 2x+4y-z=0 Normal vector of the given plane will be 2, 4, -1

Q: Find the second-order partial derivatives of the function. Show that the mixed partial derivatives…

A: Given: Now, fxx=∂2∂ x2x5+x2y2+y5+x+y    =∂ ∂ x5x4+2xy2+1    =20x3+2y2 fyy=∂2∂ y2x5+x2y2+y5+x+y…

Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an…

A: We find the local extrma using first derivative test by checking the nature of f'(x) at different…

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Q: Consider -(x Using a suitable trigonometric substitution, the resulting integral in terms of 0 is…

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Q: Find the average rate of change of the function over the given interval. R(0) = 40 +1; [6,12] AR…

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Q: Let C be a curve that is defined by x = 4 sin t and y = cos t, t e [0, 27). Determine (a) the time…

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Q: (a) Estimate the area under the graph of f(x) = 5/x from x = 0 to x = 4 using four approximating…

A: According to our policies we are allowed to solve one question at a time kindly repost other problem…

Q: 32 (c) Show that Hence, find the interval for x that satisfies the inequality = 22* 2 x 4" 32" -…

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Q: TRUE OR FALSE. Consider the parametric equations of a cycloid given below. Its length of arc is…

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Q: 3x² +7x+28 f(x) x2 + x+7 A Using partial fraction, evaluate x3 + x2 +7x aX the decomposed fraction…

A: The objective of the question is evaluate the indefinite integral in partial fraction.

Q: Integration by Parts Example 4. Evaluate In x dv,

A: The given integral is: I=∫lnxdx   As we know that; ddxlnx=1x

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Q: x +6 (a) Find dx. (1– 2x)(x² +3)

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Q: Find the function f(x) such that f''(x) = 6x + 3 cos(x), f(0) = 5, and f(1) = 2 − 3 cos(1).

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Q: 1. 4x dy – y dx = x²dy %3D

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Q: dx Using Trigonometric Substitution find f(e) - 3 (x² + x + 1)7 3 sec e 4 4 3 sec? e O 3 sec? e 4 4…

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Q: Find the first and the second derivatives of the function. y%3D 6-x

A: The given function is: y=x6-x  =-xx-6  =-x-6+6x-6  =-1+6x-6  =-1-6x-6

Q: A/Certain values of x and log1o x are (300, 2.4771), (304, 2.4829), (305, 2.4843) and (307, 2.4871),…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: 16. Follow (and show proof) of each step below to estimate the area under the curve f(x) = 3 cos x…

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Q: 4. Given [2r + 5], if r2 I = -1 and at r = 2. If discontinuous, classify the type of a. Discuss the…

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Q: 4. sin2 -x | dx. Use trigonometric groups. 2 X| cos

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Q: + Inx y(In2x – Iny)

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Q: sin COS dx V 32 COS 35 5cos² + C O 32 COS 32 + 4 COS 4 口 32 cosS Ssin+2-c cos () + c 35 4 4 32 CoS 7…

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Q: 00 Given: (1 + 2x)e*dx̟ Using integration by parts and letting dv 00 is %3D u = -1 - 2x, then the…

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Q: dx Using Trigonometric Substitution 3 sin e+C. 3 express the answer in terms of x. (x² + x + + x+1)…

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