Determine the points at which the limacon defined by the polar equation r= 3 + 2 sin(theta) has horizontal and vertical lines. Sketch the graph and show these tangent lines.

Q: Evaluate the following indefinite integral. 10 10 11x dx 10 X

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Q: Convert the polar coordinates (0,23°) to Cartesian coordinates. (0, 0) (23, 0) (0, 23)

A: Explanation of the answer is as follows

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

Q: ||r(t) × r"(t)|| ||r()* Use the formula k(t) to find k(t). r(t) = 8 cos(6t)i+8 sin(6t)j+ 7tk K(t) :

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Q: 4.x 2x 7e lim 1- e4x

A: We have to find limx→∞ e4x-7e2x1-e4x.

Q: Convert the polar equation r sing = 5 in Cartesian equation form. %3D O xy + y? = 5 x = 5 Oy = 5

A: Here we have to convert the polar equation into Cartesian equation.

Q: Suppose that f(x) = 3iV4x?² + 2 (A) Find all critical values of f. If there are no critical values,…

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Q: Question For the equation given below, one could use Newton's method as a way to approximate the…

A: We have to find the value of xn+1.

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Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Determine whether the series is convergent or divergent. If it is convergent, find its sum. (If the…

A: Yes the series is convergent. It's sum is 2/5. See below the calculation

Q: x? V1-x2 dx Use trigonometric substitution

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A: Given query is to find the number of cars between 6 to 8 am.

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Q: 2.

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Q: Q.3 - Evaluate |sec xtan.x dx.

A: As we know that ∫sextanxdx=secx+Cand dsecxdx=sectanx

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Q: Convert the polar coordinates (2, 57) to Cartesian coordinates. O (1, -V3) O (-1, v3) O (-V3, 1)

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Q: 1 1. X CasCx y) dxdy. 0.

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A: Given problem:- A street light is at the top of a pole that has a height of 17 ft. A woman 5 ft tall…

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A: Given query is to find the derivative if the expression.

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A: Given problem:- Find the critical number of given function h(p) =(p-5)/(p2+7)

Q: -3 if x 2 4 -5 -4 -3 -2 2 3 5 -1 -- 4 -2 -3 -4 -5-

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Q: Find the length of one arc of a cycloid generated by a circle of radius R = 6. Hint: Use the…

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Q: Select all that apply. Complete the general solution to y = arcsin -3. y = _+2k 3 5л O O O

A: Solving

Q: Express the polar coordinates (-2, -7) as Cartesian coordinates. (2, 0) (0, -2) O (0, 2)

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Q: f(x) Let lim = 2. Find limits below. f(x) + 6x (a) lim 2.x f(3x) (b) lim I+0 5x

A: Use the limit given above and simplify limit for a and b .

Q: is this true or false the average rate of change between any two points on the graph y=2x+7 is 2

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Q: x2+x+1 2x2+2+x3+x

A: Solution: ∫x2+x+12x2+2+x3+xdx factor the denominator ∫x2+x+1x+2x2+1dx

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Q: Consider the function f(x) = 5x³ 8x2 + 5x – 3. An antiderivative of f(x) is F(x) = Ax* + Bæ³ + Cx² +…

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Q: Match each graph with its equation. y = Vx 5+ 4 O y = Y® O y = |x| 1 O y = а. -5 -4 -3 -2 -1, I 2 3…

A: Given:    Equations is given

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Q: F- dr in the case when F(z,y) = (7y -sin (y) + 8) i+ (72 - cos (y))jis conservative, and Ais the…

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A: First take the origin and find v &amp; w vectors then solve each part.

Q: 3.) S, t°(1+ t*y°dt 4.) (x²-5x)e*dx 5.) S(4x²-7)dx/2x+3

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Q: onsider the polar curves C1 :r = 1+ cos 0 and C2 : r = 2 cos 0, and let R b

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Q: Express the Cartesian coordinates (-3, 1) as polar coordinates. (2, 330°) O (2V2, 150) O (2, 150)

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Q: Find the equivalent DE for the given family of curves All vertical parabolas

A: Find the equivalent DE for the given family of curves All vertical parabolas

Q: | (In x)? dx. 1. Use integration by parts.

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