Find a "cartesian" equation for the circle which is given by the polar equation r = 2 sin 0, and find the center of the circle.

Q: Find the length of the curve x = t³, 312 y = ²2² ²²₁ 0 ≤ t ≤ √3 t²,

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Q: mpute the following integrals using suitable method. [xy dxdy, where R is theregion bounded by y=1,…

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Q: 28-30) Given f(x) = 2x + 3 and g(x) = 3x + 5 28. If P(x) = f g then P' (2) = 29. If D(x) = then…

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Q: What is the median of the following list of numbers? [4, 12, 12 6, 10, 3] Number

A: given numbers  4,12,12,6,10,3first step is to find median is to sort our dataset from lowest to…

Q: Write the sum without sigma notation. Then evaluate. 6 Σ sin kn k=2 Write out the sum. 6 Σ sin kn =…

A: Given series ∑k=26sinkπ

Q: Find the Taylor series expansion of f(x) = = = at

A: we have to find taylor series expansion of f(x)  f(x)=1x2= x-2   at  a =1   now ,    f(x)=x-2…

Q: Express the following limit as a definite integral. n 1 lim Σ -Ax where P is a partition of [2,4]…

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Q: uestion 1: For the graph of the circle below whose equation is of the form (x-h)²+(y-k)² = r2, enter…

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Q: 4- Say whether each given sequence is a geometric sequence, or not. Find the common ratio and the…

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Q: Use Right-endpoint Rule with n = 5 to approximate ²x x√x+2dx to 4 decimal places.

A: INTRODUCTION:  The height of the approximating rectangle is calculated using the right endpoint of a…

Q: Find F'(x) given F(x) = f ³² z S³ z³ dz. <-3x ○ F¹(x)= 54x³ ○ F'(x)=0 ○ F'(x)=81x³ ○ F'(x) = 162x³

A: fiven  F(x)=∫-3x3xz3dzwe know  ∫zndz=zn+1n+1+cdxndx=nxn-1

Q: Find the limit of f(x) = lim f(x)= -7+- X as x approaches co and as x approaches -8. lim f(x) = X→∞0…

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Q: When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.01 cm/min.…

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Q: Determine the values of constants a, b, c, and d so that f(x) = ax³ + bx² + Determine the values of…

A: Given,            fx=ax3+bx2+cx+d has a local maximum at the point 0,0 and a local minimum…

Q: Determine the solution of the following differential equation d) xy' + (1+x)y = ex sin(2x)

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Q: 32. The radius of a circle is increasing at a constant rate of meters per second. What is the rate…

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Q: Find the area of the region bounded by the graphs of the equations. f(x)=sin(2x), g(x) = cos(x), -…

A: Please see the below picture for detailed solution.

Q: Consider the function f(x) = 6x2−4x+ 5 and the interval 1 ≤x ≤6. Find the number c that satisfies…

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Q: f(x) = (2x³ + 8), (1, 100)

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Q: (From Briggs) 1. Without evaluating integrals, explain the following equalities. a. b. 7(8-2x) dx =…

A: We need to explain inequalities. As per Bartleby guidelines we can solve one question from multiple…

Q: Differentiate the function. 1 g'(x) ॥ g(x) 1 2x 2 = = VX + X 1 5.( ) *

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Q: 1 1 1 은 관 + dt

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Q: 8. The following table shows the number of Facebook members f(t) in millions over time t, where t =…

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Q: Find the general solution of the D.E. (4D³ − 3D+1)y=0. Ⓒy=c₁e²x+c₁₂e-²x Ⓒy=c₁₂e-*+c₂e² Ⓒy=c₁e²+c₁₂e…

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Q: 14. Given g(x) = f(t². + 6t16) dt, find intervals on increasing / decreasing and concave up/ concave…

A: The given integral function is: g(x)=∫-22x t2+6t-16 dt

Q: -X 17) y=e^· cos(2x); dy = ? -X A) -ex (cos 2x + 2sın 2x) B) e (sin 2x- ccs 2x) c) 2ex Sin (2x) -X…

A: Given:- y=e-xcos2x

Q: ble answers No Answers Chosen The range is all real numbers. ous The equation of the asymptote is x=…

A: We will find the required.

Q: v = {3,k,-2} and w = {-2,1,2k} What value(s) of k are the vectors v and w perpendicular?

A: To determine the value of k for which the vectors v and w are perpendicular.v=3, k, -2 and w=-2, 1,…

Q: 4. Trace the curve: y² = x²−4x−12 x²-2x-3

A: for x intercept put y=0for y intercept put x=0y2=x2-4x-12x2-2x-3

Q: (n^ + n)(n^ − n) = (n)H = H'(u) = Differentiate.

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Q: Find the area of the shaded region. Ay 121- 99- 77- 55- 33- 11- y=121-x² -33- -55- -77- -99- -121- X…

A: To find the area of the shaded region.

Q: Topic: Time Rates: Inverse trigonometric functions A balloon leaves the ground 500 feet away from…

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Q: The region between the curve y = √x, 0 ≤ x ≤ 4, and the x-axis is revolved about the x-axis to…

A: Given y = x0 ≤ x ≤ 4 as we know that volume pf solid bounded by revolution of y = f( x ) V =…

Q: U. Solve the given equation 1) sec x(2 sin x-√2)=0 T Answer: x==+2nk, 4 TT ak 3π x== +2 4

A: Given query is to find the solution of the expression.

Q: 4- Say whether each given sequence is a geometric sequence, or not. Find the common ratio and the…

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Q: Use left endpoints and 10 rectangles to find the approximation of the area of the reg Round your…

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Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

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Q: find either lim 5x3 x→∞ ex one that takes less time!) Find lim (1 +5)* X→∞ 5x3 x→0 ex-1 or lim using…

A: As per the rules we are supposed to answer the first question and rest can be reposted.

Q: Use the Divergence Theorem to calculate the flux of F across S, where F = zi+yj + zxk and S is the…

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Q: Which of the following functions has a horizontal asymptote at y = 7x - 1 8x + 1 Oy= Oy= Oy= 3x² 5 -…

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Q: Find the derivative of the function. y = sin ¹(cos-¹(t))

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Q: 23) Find values for a, b and Y in Y dx to represent the shaded area below. y = f(x)

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Q: Find the limit (if it exists). lim f(x), where f(x)= x+1- [x³ +2₁ x < 1 x+2, x ≥ 1

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Q: 18 Suppose c is directly proportional to the square of d. If c when d = 3, find the constant of…

A: given that , c is directly proportional to the square of d ⇒ c α d2⇒c = k d2 ................(1)…

Q: Determine the solution of the following differential equations. a) (D² +9) y = 81x² + 14cos3x

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Q: (b) Given the graph of f (x) below (blue), select the correct graph of the transformation y = 2f (x)…

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Q: The general term of a sequence is given. Determine whether the given sequence is arithmetic,…

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Q: Find the slope of the tangent line to the curve x=t+ 1, y=2t² + t -1 at t= 1.

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Q: Find the slope of the function's graph at the given point. Then find an equation for the line…

A: Given query is to find the slope and the equation of the tangent.

Q: Find the derivative of the function. y = sin ¹(cos ¹(t))

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