Find the limit of the following sequence or determine that the sequence diverges. (-1)^) 4n+3

Q: Integrate (3-2)¹0 dar Select one: OA.(3-2)¹¹ +C OB.(3-2)¹¹ +C 12 OC.(3-2)¹¹+C OD.(3-2)¹¹ +C 10

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Q: Let f(x)=√x - 7. Then lim h→0 f(3+h)-f(3) h 1 2√3 If the limit does not exist enter DNE.

A: Laplace transform:- If limh→0f(h)g(h) is of the form 00 then limh→0f(h)g(h)=limh→0f'(h)g'(h) and so…

Q: Use the formula for the general term (the nth term) of a geometric sequence to find the indicated…

A: We can find the 5th term as below.

Q: Question 1 Let C be a curve defined by the vector equation r(t)= <8t³ - 9t, 8t³ +7t, e8³-917. Show…

A: Solve the following

Q: Solve using variation of parameters: y" - 2y + y = ¹/(1+t²) + 3e¹ Type the letter of your answer. Yc…

A: Given :y''-2y'+y=et1+t2+3et

Q: Workout Problem j Part a: ( 1. Find the domain of the vector function r(t) =

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Q: Rewrite the expression as an equivalent expression that does not contain powers of trigonometric…

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Q: Use implicit differentiation to find dy/dx. b. Find the slope of the curve at the given point.…

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Q: Evaluate the integral [x x cos x dx

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Q: Work problem 3 Given the vector function () 5 F(t) = (6t³ · (61³ – —‚ t - sec(4 – t)), then find the…

A: We have to find the tangent vector at t=4.

Q: Work Problems ( your works 1) Let F(t)=(4t — t²)i+t² j+sin(5t — 10) k - - - You need to show all a)…

A: Given: Ft=4t-t2 i+t2 j+ sin5t-10 k

Q: Calculate the integral where R is the region inside x ^2 + ?^ 2 = 4? and external to x ^2 + ? ^2 =…

A: We have to calculate the integral.

Q: Find the power series representation of the following functions 3x (a) f(x) = 2x+7

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Q: If f(x, y, z)=√x²y² z², then fxyz (x, y, z) = 2xyz √x² 1² z² Select one: True O False

A: We have to state if given statement is true or false.

Q: Solve the following triangle. B = 70°, C = 50°, b = 8 O A (Simplify your answer.) a≈ (Type an…

A: We will use law of sines to solve this question.

Q: A rate of change of H is given by Solve for k where H > -25. O 0.458 O 0.346 0.255 O 0.144 dH = k…

A: topic- differential equation

Q: 4. Find the power series representation centered at 0 for f(x) = 8x 2+x³

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Q: Find the limit of the following sequence or determine that the sequence diverges. 2n² 1 6n² + 1 -…

A: Solve the following

Q: √(√3+)dx Select one: OA. OB. OC. OD. ³/2-² + 4x¹/2 + G ³/2² + 4x¹/2 + G ³/2² + 4x¹/2 - ³/2x² + с +…

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Q: The rate of change of N is inversely proportional to CSC(x) · N(x), where If N () = 1, and N (5) =…

A: Given: dNdx∝1cscx.N

Q: Set up the definite integral required to find the area of the region between the graph of y = = x² y…

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Q: 2. Approximate In (0.93) using a Taylor polynomial with n = 3. Round your answer to seven decimal…

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Q: Choose the normal vector of the tangent plane to the surface defined by at the point (-4, 2, e88). O…

A: Given problem:- Find the normal vector of the tangent plane to the surface defined by…

Q: Estimate Ay using differentials. .1/3 y = x¹/3 e³x-1, a = 1, dx = 0.1 -

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Q: Sy²sin (2y) dy

A: Integration by parts.

Q: Use the formula for the general term (the nth term) of a geometric sequence to find the indicated…

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Q: The graph of the first derivative f' of a function f is continuous on (-∞0,00). -2 -1 2 3 (e) Find…

A: The graph of the first derivative f' of a function f is continuous on -∞, ∞. e To find the…

Q: Find all relative extrema. Use the Second Derivative Test where applicable. (If an answer does not…

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Q: The domain of the function f defined by is equal to: Select one: O True O False 7 cos(x)+y² In…

A: This question is based on logarithmic function.

Q: For the following exercise, use logarithmic differentiation to find dy dx y=xcotx

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Q: dy Find ck by implicit differentiation. √x+ y + √xy =4

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Q: dy=(x-2ycot 2x dx

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Q: 13. Express H(x): = 14. Express H(x) = 2x-1 as a composition of two functions f and g where H(x) =…

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Q: Apply the Mean Value Theorem tof on the indicated interval. Find all values of c in the interval [a,…

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Q: -5 -3 2-1 3+ 1 1 2 4 N -1 B 2- Submit Question ON 4+ 10. -3 Which of the following is true about = 0…

A: Let's find true statement about given graph.

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of PQ.…

A: Here we have to find the directional derivative.

Q: Use the formula for the sum of the first n terms of a geometric sequence to solve. Find the sum of…

A: The given geometric sequence: 32, 38,332,.....

Q: Find the coordinates of the center, foci, vertices, and the equations of the asymptotes of the conic…

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Q: If the given sequence is a geometric sequence, find the common ratio. 4/3, 8/3, 16/3, 32/3, 64,3

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Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations.…

A: We have to find area of given region.

Q: A polynomial f(x) and one or more of its zeros are given. f(x)=x²-2x³+3x²+4x-10 1-2i is a zero

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Q: 25. If f(5) = 2, then f-¹(2) =

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Q: Find critical value -5x^3+15x+3

A: This question can be solved using the concept of critical points of a function.

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y(4) +…

A: We have to find the suitable form of Y(t).

Q: Find the first partial (a) derivatives of the function f(x, y) = x²y√√√y + 4y². (b) fxyx of the…

A: A two variables function f(x,y) is provided. We have to find the first partial derivatives and…

Q: Let lim f(x)= -20 lim f(x) = 20 lim f(x) = DNE f(4) = 1 [–52, £ 4. Is f continuous at = 4? (YES/NO)…

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Q: The temperature in degrees Celsius on the surface of a metal plate is given by T(x, y), where x and…

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Q: B a A b LI Use the right triangle and the given information to solve the triangle. a = 1, c= 2; find…

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Q: The area of the ellipse is given as A = ab. Find the area of the ellipse 25x² +16y² - 100x + 32y =…

A: given equation of ellispe 25x2+16y2-100x+32y=284

Q: Which of the rectangles below are right rectangles? 25-4 20 15 10 63 BODEX 0 5 10 15 20 25 Select…

A: This question can be solved using the concept of estimating the area under curve using left and…