Evaluate 1 2. tht Htte tan e(:-+) 2 , у акуся, whve с is the contour given by

Q: IV. Fill in the blank to make each statement true. Use correct notations. 12π ¹ (sin ¹2) = 5 1. sin¹…

A: We can find the answer in the following steps.

Q: Find the derivative of y = 3x² + 5x- 2 from first principles.

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Q: Find the average value fave of f(x) = x5 between -1 and 1, then find a number c in [-1,1] where f(c)…

A: We have to find the average value of function and value of c.

Q: (a)Show that F is a conservative vector field. f(x,y,z) = (b)Find a potential function for F.

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Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: 4 3 1…

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Q: If z² - 3yz² + xyz -2=0, find Az дz and дх ду

A: The objective is to find the Partial derivatives.

Q: Water is leaking out of an inverted conical tank at a rate of 11700 cubic centimeters per min at the…

A: Let's find rate of water is being pumped into the tank.

Q: Determine whether the series converges or diverges. ∞ 7" 5 + 12" n = 1 The series converges by the…

A:

Q: Find the Fourier series for the following functions: f(t) = |sin t], -1 < t < n

A: To find the Fourierseries for the following functions.ft=sin t, -π&lt;t&lt;π

Q: Find an equation for the ellipse whose vertices are at (-8-2) and (0-2), and focus is at (-2-2)…

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Q: Use the Root Test to determine whether the series converges. 2 1 3 1 1 ·* ·*·* ... + 18 36 54 72 +…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: What type of graph is this? A parabola An absolute value graph A hyperbola A linear graph

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Q: Fill in The Unit Circle Positive: Negative: Positive: Negative: O O Positive: Negative: Positive:…

A: The unit circle is,

Q: Which of the following shows the expansion of 2-5n? n-0 O(-18) + (-13) + (−8) + (−3) + 0 O(-3) +…

A: To find the expansion of the given expression, substitute n=0,1,2,3,4 in the given expression.

Q: Which of the following statements proves the series-128+96-72+54- O 2 is geometric?

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Q: Use the Divergence Theorem to evaluate F. ÑdS where F(x, y, z)=x²i +2y²j+z²k S and the surface S is…

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Q: What is the explicit equation for the nth term of the arithmetic sequence 6, 3.5, 1,-1.5, 4,...?…

A: We have: a1=6 -- the first term   Next, we calculate the common difference d=a2-a1 So, we have:…

Q: Find the derivative of the function. y = sin (7) + √sin (6 x) y'(x) =

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Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 25x2 +…

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Q: Then S-4 -√25-x² 4xy dy dx = Graphs: sketch the region of integration and evaluate the integral.…

A: The objective is to  solve the above question.

Q: ) cos(cos-¹(35)) ) sec(tan-¹(5)) csc(sin-¹(n)) ) cos ¹(cos(29°)) (4π) 5 =) sin ¹[sin ]]

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Q: Determine the open intervals on which the graph is concave upward concave downward. (Enter your…

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Q: D Question 24 Suppose that P= f(t) is the population (in millions) of the country & years after the…

A: We can find the answer as below.

Q: Find an equation for the tangent plane to z = f(x, y) at (3,-2) if the differential at (3,-2) is df…

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Q: What are the coordinates of the x-intercept of the equation 2x - 3y = 8? (-4,0) (-8/3,0) (0,-8/3)…

A: Please see the below picture for detailed solution.

Q: price

A: At Equilibrium, Demand = Supply,

Q: Which one of the following equations could work for the following graph? y = 5 y = -5…

A: To find,  the equations could work for the given graph.

Q: The hyperbolic orbit of a comet is represented on a coordinate plane with center at (0,7). One…

A: Given hyperbola, Centre (h,k)= (0,7) Vertex = (0,4) Foci = (0,2)

Q: Calculate the double integral √ √(8x + 2y + 16) dA where R is the region: 0 ≤ x ≤ 1,0 ≤ y ≤ 4.

A: The objective is to evaluate the double integral.

Q: Estimates of  ∞ n = 1 1 n2  can be accelerated by writing its partial sums as  N n = 1 1 n2  =  N…

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Q: 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

A: I have stated the used formulas in the solution

Q: Which of these equations represents a line that is perpendicular to the line in the graph below?

A: Two lines are perpendicular if the product of their slopes is equal to -1

Q: Consider the system of differential equations dx dt x(t) y(t) -2y Convert this system to a second…

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Q: The graph of a function f is given. Use the graph to estimate the following. y W 2 3 (a) All the…

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Q: Question 14 Each side of a square is increasing at a rate 3 in/s. At what rate is the area of the…

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Q: y (az + √2) sin (ay²) dy + (az − √√2) dz = 0 4√2 ln az + √2 = C 4√2 In az + √2 = C 4√2ln az + √2 = C…

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Q: Use an appropriate test to determine whether the series converges. 2(k!)4 9(4k)! Σ k=1 By the this…

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Q: The y-coordinate of the vertex of a parabola that opens up is called the _____. minimum value…

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Q: Find two positive numbers satisfying the given requirements. The product is 182 and the sum is a…

A: Topic- Quadratic equations

Q: Evaluate the following limit: lim+1 x+1 01 2 02 Oc undefined

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Q: B Fig 1 1 y = (3x)3 A I. Find the co-ordinates of A and B X II. Find the area enclosed by the curves…

A: Please see the below picture for detailed solution.

Q: an = {( – 2)"} a) Find ag b) Find Σ.,a, 1 an 4

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Q: Find an equation for the ellipse. Graph the equation. center at (3,-2); vertex at (8,-2); focus at…

A: We need to find equation of ellipse.

Q: Express the given quantity in terms of −sin x or cos x. sin(3ℼ/2 - x)

A: The given trigonometric function is f(x)=sin3π2-x

Q: 8) About the y-axis (0, 2) л y = 2sin (x) ;0< x≤ π X X

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Q: Use the shell method to find the volume of the solid generated by revolving the shaded region about…

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Q: below is conservative and find its poter 3x²e³y +15y²z+2x²yz²)j + (5y³ + 2x²

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Q: Differentiate y = (2x³ + 3x² - 1)5 5(6x² +6x)4 30x(x+1)(2x³ + 3x² - 1)4 30x(x + 1)(2x³ + 3x²-1) O…

A: The given function y=2x3+3x2-15 we have to find the derivative of the function

Q: A function is given below. Determine the average rate of change of the function between t = 6 and t…

A: The objective is to determine the average rate of change for the function.

Q: Use the Root Test to determine whether the series converges. 3k² k Σ k+4 k=1 Select the correct…

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