Find the first five terms of the given recursively defined sequence. 2an - 1 + 6 and a₁ = 2 n- a₁ a2 = а3= a4 a5 || II || an =

Q: 3 Solve the following GDES by variation of parameters method: ý - 2y +y = e sinx Ansa U ● X sin X

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Q: Maximize f(x, y) = √11-x² - y² Constraint: x+y=2=0 )

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Q: 3 dx 00 (2²+4)³/2 es or diverges.

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Q: 20. Find the area of the region outside the circle r = 3 and inside the circle r = 6 cos 0. -2 0 -2-

A: Given curves are r=3 and r = 6cosθ  At the point of intersection , we have…

Q: 1.12 Evaluate the limit, if it exists. If not, enter "n" below. x²+x-6 x - 2 lim I-2

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Q: Verify Green's Theorem for: f4y³dx-2x²dy where C, oriented anti-clockwise, is composed of the…

A: To find the integral ∮C4y3dx-2x2dy where C is the positively oriented closed curve x2+y2=9, y≥0 and…

Q: Evaluate the following definite integral. 5 dx 2 0 √x + 169

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Q: Find the coefficient of the term x6y³ when the expression (x + y)⁹ is expanded by the binomial…

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Q: Find the angle between the vectors in radians and in degrees. u = 8i + 3j + k v = 3i - 8j (a)…

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Q: Determine whether the series +∞0 [[CDS-¹ (-)-CO₁¹ (1) Σ|cos -1 -1 n=1 converges or diverges. If the…

A: This is a problem related to series and sum calculation. Please find the procedure given below.

Q: How did he get the value inside the circle by ===//= √xlt) sin (nwot) dit bn cl 11 2 (= (₁-7) Sin…

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Q: We are trying to prove the following limit. 1 Suppose that we have found a value of & such that e =…

A: According to the ε-δ definition of limits says that the limit of f(x) at x=c is L if for any ε>0…

Q: Determine whether the following series converges. Justify your answer. Σ k=1 k! K+14

A: This is a problem related to series and sum calculator. Please follow the procedure given below.

Q: The angle between 0 and 360° that is coterminal with - 119° is

A: To find out the coterminal angle of -119 degrees.

Q: Using tabular integration, the integral In 2 S™ (-2x + 1)e²x dx is equal to

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Q: What value(s) of 8 are an appropriate choice when proving the following limit? lim (x²+x-14) = 6…

A: To prove  limx→-5x2+x-14=6 , we need to prove that    for any ε>0     ∃  δ>0  such that…

Q: -2 - 1 How did he get the value inside the circle 1-t x (t) = ૧ 1-t 2

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Q: A vendor at a carnival sells cotton candy and caramel apples for $2 each. The vendor is charged $175…

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Q: Determine if the geometric series converges or diverges. If a series converges, find its sum. 2 1 1…

A: Given the series, 18+182+183+184+185+........

Q: 6. Find y" give y = 7³x a) 21³x In(7) b) 63³x In(3) c) 3(7³x)ln(3) d) 9(7³x)(ln7)

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Q: For the graph below, identify a restricted domain for which the function has an inverse that is also…

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Q: Graph the function. g(x) = 8 x²-16 Plot at least two points to the left and right of each vertical…

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Q: If you invest $1200 with interest compounded weekly (52 times per year) at 3.7% for 6 years, how…

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Q: 1.16 Let f(x) = lim_f(x) = H-4 2, 4x + 19, Calculate the following limits. Enter DNE if the limit…

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Q: Find the directional derivative of the function at point P in the direction of v: f(x,y)=x^3 y,…

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Q: & 5 im 4 32 1 -2 0-3 -4 im →-1- f(x) = f(x) = _m f(x) -1 - − 1) =

A: Topic:- calculus

Q: Consider the following repeating decimal. 0.5 Exercise (a) Write the repeating decimal as a…

A: Consider the following repeating decimal. 0.5To write the repeating decimal as a geometric series.

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Q: The graph of y=f(x) is given. Solve the inequalities. Write the solution set in interval notation if…

A: Consider the graph of the function

Q: waluate the following integral. 2 3x dx (16+x²)²

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Q: Determine whether the given function is linear. If the function is linear, express the function in…

A: Given question:- Determine whether the given function is linear. If the function is linear, express…

Q: The cost of producing 420 calculators is $2320. Producing 580 calculators would cost $3120. Step 1…

A: The cost of producing 420 calculators is $2320. Producing 580 calculators would cost $3120. To find…

Q: What does the slope of a secant line through two points on the graph of a distance vs time graph…

A: lets consider

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Q: 1. Let f(x, y) = y³ + x³ - 2y² - 3x + 30y. (a) Find all the critical points of f. (b) Determine…

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Q: 1. Use the substitution method to evaluate x² S. VAI ³ + 50° dx

A: Here we have to find the integral using substitution method.

Q: 5. Evaluate 8y L L (PS4 12 dzdy + 1)² by reversing the order of integration.

A: Follow the procedure given below.

Q: 4) lim (1 + sin 4x)¹/x x→0+

A: Given limx→x+1+sin(4x)1x

Q: Evaluate using integration by parts o a) (In 3x dx

A: As per the rules of the company we can only the first question and rest others can be reposted.

Q: Find the solution of the given initial value problem: y(4) + 2y""+y" + 8y′ − 12y = 6 sin(t) + 80e¯t;…

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Q: Find the directional derivative of the function at P in the direction of Q. g(x, y, z) = xye⁹², P(2,…

A: Given :gx,y,z=xye9zP2,2,0, Q0,0,0

Q: 1. What is the average rate of change of the function f(x) = x² - 4x + 7 on the interval 1 ≤ x ≤ 3?

A: average rate fo change in an interval (a,b) =f(b)-f(a)b-a

Q: 2. Determine the intervals of increasing and decreasing, critical numbers, and classify relative…

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Q: Integrate using partial fractions o 5x² (x²+3)(x²-4) Si dx

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Q: Shown is a graph of y=f(x) a) what is the transformations In the appreciate order of how to make a…

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Q: Write an equation for the transformed logarithm shown below, that passes through (3,0) and (0,3) -5…

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Q: Let 8 f(x) = ΣX2 n = 1 Find the intervals of convergence for f. (Enter your answers using interval…

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Q: 9. Estimate the value of the convergent series 8 k=1 (-1)^² k! + 2k with an absolute error less than…

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Q: 11 7 Find Y 12 2r₁²³² + y² = 4 2

A: here is the solution