2. The limit of the following function equals: a. 0 b. 1 c. -1 d. None of the above answers x2/3 + x-1 lim X-400x2/3 + cos²x

Q: Q1: A-Show if the series is convergent or divergent (2n)! n!n" n=1

A: This question is related to infinite series, we will solve it using given information.

Q: (a) Σ(1/7)", (b) (1/7)" where k is a nonnegative integer, n=k (c) Σ07" /n!, n=0

A: We have to evaluate the value of series in this question.

Q: Let f(b) 24 4 b-3 6²9 Evaluate the limit: lim f(b) b-3 21|00 3 ९ 8

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Q: 4. Show that both x₁ (t) = et cost and x2(t) = et sint are solutions to the second-order…

A: To show that both x1t=e-t cos t, and  x2t=e-t sin tare solutions to the second‐order differential…

Q: Graph the following system of equations. x - 4y= -1 4x-3y=6 Use the graphing tool to graph the…

A: To graph the given system of equations

Q: On the graph shown, what is f(2)? Y 000 -1 02 3 CJ 7 4 C-C x

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Q: 2. At what point does g(x)= have a removable discontinuity? A. x=8 B. x= 8 C. Nowhere D. x= 1 E.…

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Q: 12. Find the antiderivative of the following expression: sin (x)] 6sec (x) - 12cse' (x)] A. 6sec (x)…

A: Integration formula ∫ (cosec2xdx) =-cotx+c ∫xndx=xn+1n+1+c

Q: 4. lim-0 A. B. 1 C. sin D. Does not exist E. -1

A: We need to find limit.

Q: 1. Using the graph of f(x), what is lim, -1/(x)? A. - 00 B. 0 C.-2 D. Does not exist E.

A: As shown in figure, As x tends to -2 from left , f(x) tends to negative infinity . That is…

Q: If a parametric surface given by r₁ (u, v) = f(u, v)i + g(u, v)j + h(u, v)k and -2 ≤ u ≤ 2, -3 ≤ v ≤…

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Q: e x² + y² = z², bounded below by the xy-plane and bounded al integral to find the surface area of S…

A:

Q: 2. On February 10, 1990, high tide in Boston occurred at midnight. The water level at high tide was…

A: Given 1. High tide at midnight t=0. 2. Water level at high tide = 9.9 feet. 3. Low tide at 12 noon…

Q: Calculate the Taylor polynomials T₂(x) and T3(x) centered at x = 0 for f(x) = sin(x). (Use symbolic…

A: The given function is f(x)=sin(x) Here we have to calculate the Taylor polynomials T2(x)=? and…

Q: Solve the equation by factoring or the Quadratic Formula, as appropriate. (Enter your answers as a…

A:

Q: Given the DE as 2xy² + 4 = 2(3-x²y)y'. A. prove or disprove if the given D.E. is exact. B. If it is…

A: The given differential equation 2xy2+4=23-x2yy' Exact differential equation:    The differential…

Q: A graphing calculator is recommended. For the function, consider the following. g(x) = 9*; find…

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Q: 3. What is the general term of the sequence: 5, 15, 45, 135, 405, ... a. t₁ = 3(15) b. t₁ = 3(5)n-1…

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Q: an equation of the tangent line to the graph of "f" at the given point: y=x3-3x+1, (2,3)

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

Q: If you use the ratio test on the divergent series inequalities will result? A. lim,- >1 > 1 1 >1 81…

A: Topic:- sequence and series

Q: 28. The value of In (2) can be calculated by the alternating harmonic series. In (2)-1-+-+ Using the…

A: Here is the solution:

Q: Write the equation of the circle centered at ( – 6, 1) that passes through (16, - 16).

A: Topic:- geometry

Q: Consider the vector field F(x, y, z) = (yz, 9xz, —xy). Find the divergence and curl of F. div(F) = V…

A:

Q: 2. -4 (a) f(-1) (c) f(0) -3 -1 *** y 1 -1 -2 -3 (b) f(2) (d) f(-2.5) 1 3

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Q: For the given functions, write formulas for f of g an g of f and find the domain of each f(x) =…

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Q: {(1, 2), (2, 5), (3, 7), (1,3)} {(3, 3), (4, 5), (5, 11), (6, 13)] 9. 10.

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Q: Find the integral. (Note: Solve by the simplest method - not all require integration by parts. Use C…

A:

Q: Evaluate the integral using the following values. 6 6 6 fox Lº Sº dx 4 4 x3 dx = 260, x dx = 6 [²…

A:

Q: The height y (in feet) of a ball thrown by a child is 1 -x² + 4x + 5 Y 14 where x is the horizontal…

A: Topic:- calculus

Q: Determine the symmetry with respect to the ?-axis, ?-axis, and the origin for the given equations.…

A:

Q: Find equations of the lines through the given point parallel to the given line and perpendicular to…

A: To find out the equation of line that passes through the given point and parllel and perpendicular…

Q: olve the initial value problem dy ¹y = x² + 3 + e²x, y = −1 when x dx

A: Topic:- differential equations and integration

Q: -1 If cot (sin-¹ √√1-x²) = sin (tan¯'(x√6)), x ±0 then the value of x is.......

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Q: From the top of a 220-ft lighthouse, the angle of depression to a ship in the ocean is 26 degrees.…

A:

Q: Find the average rate of change of the function from x=1 to x=4 of f(x)=-8/x^2

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Q: where did you get 48?

A: The supply function Sx=5x+8 and the demand function Dx=120-9x we have to find the equilibrium point

Q: 6.5+ (y)² = [3z³y² + (y")³14/3

A:

Q: iF w=f(x-y₁ y-Z, Z-x) then dw dw dw = ? dx dy dz Chain roll

A: Chain Rule : If w= f(a,b,c) and a=g(x,y,z) ; b= h(x,y,z) and c= l(x,y,z) then…

Q: does the series  E infinity/n=1  2^n/3^n converge or diverge a)the series converges because its is…

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Q: Find domains and ranges of the following relations? Write domains and ranges in interval notation

A: We can find the domain and range from the graph in the following steps.

Q: 20. lim #45 2 = 7

A:

Q: في Lim X-1 X1 X²-1

A: Hint : Factorise denominator

Q: a) Find the area of the region enclosed by the curve y=x²-2 and by the line y = 2. y=x²-2 y=2 Co

A: Area of a closed region is given by  A=∬dydx, when the strip of area is parallel to y-axis.

Q: 11. If v = 4n²r³ and h = 4πr, find h in terms of v.

A: Given, v=4π2r3                               (1)h=4πr                            (2)

Q: Given 5x -12y-4=0 write an equation of a line through the point (-5,-2) and parallel to the given…

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Q: 1. The first derivative of the following function is: a. b. C. d. csc²(xy)+1 x csc²(xy)+1 xy y -y xy…

A:

Q: 7. Rationalize the expression. √x² + 1 -√√x

A: Rationalize expression

Q: The function x²y=4+Cy is the solution to the Differential Equation 2y'+xy²=0 Note: C is arbitrary…

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Q: Use the following function and its graph to answer (a) through (d) below. 4-X, X2. Let f(x)= a. Find…

A: Given that fx=4-x,x<2x+1,x>2Solution :

Q: what is the volume of the following demensions? length= 4.23 cm width= 1.58 cm height= 6.80 cm

A: