dx By algebraic substitution, the integral |- -dx is converted to: 4+x dy A y+4 2ydy B у+4 2 dy y+4 D y+4

Q: Convert the Cartesian equation x 2 + y 2 - 6x = 0 to a polar equation.  r² = 6cosθ r = 6sinθ r =…

A: The given Cartesian equation x 2 + y 2 - 6x = 0 ................................... (1)

Q: Solve the following equation for x (find all solutions between 0° and 360° Round answer to 2…

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Q: Write the complex number in standard form. 3-V-30 4 + 30i 3 + 30i 3 – V30i 7- 30i O 4- 30i

A: Simplify using basic concepts of complex number.

Q: Direction: Find the derivative of each of the following functions. Write your solutions on a…

A: We have to find the derivative

Q: Drection: Evalate /(2) fr the gien functons. a. -2 b. -6 d. 2 4 f)=P-4 a. 3 b. 6 c. 12 d. 2

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Q: As 2.

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Q: ASSIGNEMNT #5 Determine if the function is continuous on the indicated close interval SVx +1 (5- x 0…

A: A function y=f(x) is said to be continuous at x=a iff, limx→a-f(x)=limx→a+f(x)

Q: Find T(t) and N(t) at the given point. r(t) = 2 cos(t)i + 2 sin(t)j + tk; t = 2 T -25 i + 15 k NE) =…

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Q: Find the critical points of the following function. 14x f(x) x2 + 49 Select the correct choice below…

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Q: Show that (f) and () aoe invesse fondion ARgeboaically @ fix) fex) = " O f cx) = X- I X+5 g(x) = ニ

A: We have to show that f and g are inverse function.

Q: Convert the Cartesian equation x 2 + y 2 = 36 to a polar equation. r = 6

A: Topic = Circle

Q: x +1 8. J x(x+ 4)3 dx

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Q: Determine whether the series (-1)". converges or diverges. Vn3 +2 n=1

A: Apply Leibniz test for convergence

Q: Convert the polar coordinates (- 3, -4) to Cartesian coordinates. O (3/2/2, -3V2/2) (-3v2/2, 3V2/2)…

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Q: Which values are solutions to the equation on the interval (0, 2m)? Select all correct answers. 12…

A: The given equation,     12sin2x+4sinx-1=0

Q: Express f(x) in the form f(x) = (x-k)q(x) +r for the given value of k. f(x) = 3x +x + x-4, k= - 1…

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Q: Numerically integrate f (x) = x³ + 3x? + 4x = 2 using Single-Trapezoidal Rule. 6 from a = 1 and b -…

A: (1) solution

Q: c.) S (4t²-t²+16t)dt/(t²+4) d.) S V1-cos*o de

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Q: Sa sec ede tan' 0+9 tan e

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Q: Choose the point which shows the correct location for the polar coordinate (1, 320°). 90° wIN 135°…

A: We have to find correct point name for co-ordinate for point (1,320°)

Q: Write the integral that can be used to find the region bounded by x = -3y² + 4 and x = y³.

A: We have to construct  the integral to find the region bounded by given curves.

Q: de 6) S 7) S(1 – sin? 3t) cos 3t dt 8) ſ tan (5x) sec?(5x) dx cos? e

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Q: Determine the intervals on which the following function is concave up or concave down. Identify any…

A: The given function,  g(t)=3t5-20t4+30t3+80

Q: dx Vx3 V2 + x

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Q: Find the exact length of the curve. x = 2/3t3,  y = t2 − 2,  0 ≤ t ≤ 2

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Q: sin(en sin-lx )dr =- cos( sin-!x) +C V1-x? A) True B) False

A: To solve the following integral

Q: e4x dx Which of the following trigonometric substitutions is the most appropriate to the intgral J-…

A: Follow next step

Q: Find the radius of convergence and interval of convergencE of the power series. (x 25. E 2)" n=1 n"

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Q: B C a A Note: Triangle may not be drawn to scale. Suppose a = 10 and b = 7. Find an exact value or…

A: Follow next step

Q: If the slope of the tangent to f(x)= a(x-1) + bx at the point (2, determine the values of the…

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Q: If the terminal arm of an angle, x, in standard position passes through the point (-a, -2a) where a…

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Q: Find the acute angle in radians between the planes 1x+z=1 and 1y+z=1. You may leave your answer in…

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Q: Find the cost function for the given marginal cost and fixed cost. marginal cost= 1/80x+40 fixed…

A: Given:        Marginal cost dCdx=180x+40         Fixed cost x=0=$8000…

Q: Determine whether the lines

A: To find out that the lines are parallel, intersecting or skew.

Q: y =x, 4x + y =12

A: Let's find.

Q: Find the area, if it is finite, of the region under the graph of y = 14x° over [0,00). Select the…

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Q: find (a) f• g, (b) g•f, and (c) f • f. (i) f(x) = x*, g(x) = x - 1 %3D

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Q: а. 1 b. 5 с. -1 d. 2 2. S(x) = 3x² %3D а. 3 b. 2 с. 6 d. 12

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Q: If k is any real number, prove or disprove that sinkx 1. lim x→0 kx 1.

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Q: 7)S ) dx 8)S; dx 1+3e* 9) S 3x3. e-2x* dx

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others…

Q: To evaluate y-csc²(y³) cor²(y³)dy, we let u =csc(y³) (A) True B) False

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Q: Find the sum of the infinite geometric series 1 1 1 4 1 +.. 64 16

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Q: Determine if the following series is convergent or divergent: 3n 7n – 2 - n=1 O Convergent O…

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Q: Problem 3. The softplus function is given by A2) = log(1 + e) A) Plot ſ(2) as a function of z. If…

A: (1) solution

Q: Determine whether the function is one-to-one. If it is, find a formula for its inverse. f(x) = x +7…

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Q: #12- Fnd the indefinite integral of the follaung funchon and check the result by differentionion.

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Q: Write the expression as a logarithm of a single quantity. In(8) + In(x + 5) - 4 In(1 + Vx)

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Q: Find the intercepts, critical numbers, intervals) of increasing and decreasing relative extrema,…

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Q: Find the vertex of the parabola, y=x²+4x+1 O a. (2,13) O b. (-2,-3) O c. None O d. (-4,0)

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Q: The rate of change in the number of urban transit vehicles such as buses and light-rail trains, in…

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