Evaluate the following limits if they exist: lim In (3x-1) 5+x x->-5 e a) b) x-lnx lim x-e* lnx-1 El

Q: 5. Prove the identity: cot(A + B) cot(A − B) = cot² B tan² A tan² A cot² B - 1 3J

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Q: The legs of a right triangle have lengths 3 cm and 4 cm, respectively. A rectangle is inscribed in…

A: This question can be solved using the concept of maxima and minima.

Q: 2 s x² dx x2-4

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Q: 7. Solve for cot NI 2 if cos(20) = |L0 5 and P(0) E QIV.

A: Given: cos2θ=-45 To find: cotθ2

Q: 4. Evaluate the line integral f x siny dx + y dy, where C is the arc of r(t) = ti + t²j from point…

A: Line integral

Q: 19. Which of the integrals below represents the set-up of ff xy dS, where S is th vertices (1, 0,…

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Q: Which of the following equations describes the nth term for the sequence O (3) -1(9)*** 4 1 1 1…

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Q: 2. Sketch the solution region of 2x - y - 1>0 (x - 5)² + (y + 1)² ≤ 25.

A: The given inequalities, 2x-y-1>0(x-5)2+(y+1)2≤25

Q: 5. What is odd and even function?

A: We have to define odd and even function.

Q: I. Find the solution set of the following. 1. 2e²3e + 1 = 0

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Q: 1 ∞ Inxdr

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Q: Solve p = So (S2₁ Aedx) e dy Evaluate p assuming A closest to your answer: = 2.0 and 8 = 3.0, and…

A: Answer must be option 3.

Q: : x-2y+3z-1 = 0 and the line 1 : x = Consider the plane 1. Find the point of intersection of and 1.…

A: Given: x-2y+3z-1=0x=1-y2=z+1

Q: What is the point-slope form of the equation that goes through the origin and has a slope of 1.5? y…

A: The point slope form of a line passing throught the point (x1,y1) and has slope m is  y-y1=m(x-x1).…

Q: The table shows various values of a linear function f(x). X-40250 -4 0 2 5 9 10 f(x) -11 1 7 16 28…

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Q: The base of the solid is the triangle enclosed by x + y = 11, the x-axis, and the y-axis. The cross…

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Q: Suppose that a particle moves along a straight line with velocity v(t) = 14 - 6t, where 0 < t < 1.5…

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Q: A D 1. Determine an expression for the area of a rectangle inscribed in a circle of radius 1 cm, in…

A: Explained below

Q: Solve the given initial value problem. y'' - 4y' + 3y = 0; The solution is y(t) = y(0) = - 1 2 y'(0)…

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Q: Set-up the double integral that will solve for the volume of the solid in the first octant bounded…

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Q: 2. S (x+1)dx x²(x-1)

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

Q: Sketch the area bounded by x^2 + 2y = 4 and x + y + 2 = 0 on the image below and determine the…

A: volume of above function is π×175.19 cube unit

Q: Use the Ratio Test to determine whether the series is convergent or divergent Identify an 00 Σ (1)"…

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Q: e Find the volume generated by revolving the area enclosed by the loop of the curve y² = x (x-3)²…

A: Solution is given below:

Q: If a cup of coffee has temperature 92°C in a room where the ambient air temperature is 23°C, then,…

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Q: • 25 Which of the following graphs represents (+2 30 la T 7 17 T 49 19 15 O . 7 17 T 19 19 15 19 19…

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Q: If -2 5 [° f(x)dx = [__ * f(x)dx + [_^¸ ƒ(a)dx − [¯* f(x)dx, -8 what are the bounds of integration…

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

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Q: `11,  Find a function  f(n)  that identifies the nth term  an  of the recursively defined sequence,…

A: The solution is given below

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

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Q: Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements…

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Q: 4. S dy y³-2y²

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Q: 2 y²dx + xydy = 0

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Q: ical numbers r = -1 and x = 2 are found from a continuous derivative the second derivative is f"(x)…

A: Topic:- application of derivatives

Q: What is the equation of a line that is parallel to y = -4x + 2 and goes through the point (-4, 9)? y…

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Q: y = In z I at x = 1: Oy=-x+1 Oy=-x-1 Oy=x-1 Oy=x+1

A: As per the company's guidelines, we are supposed to solve the first question for you, kindly repost…

Q: 3. Find the domain of f(x) = 1- 1 X X

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Q: I. Find the solution set of the following. 2. 3x²+2x³7x² - 4x +2=0

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Q: On Integration of Rational Fractions. Distinct linear factors Repeated linear factors x+8 x+8 x²+x-2…

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Q: For each positive integer n, define an = n² sin 2 +∞o 1. Determine if the sequence {an} converges or…

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Q: PRACTICE ANOTHER The graph shows the depth of water W in a reservoir over a one-year period as a…

A: Topic- Average rate of change of function over interval

Q: . For each positive integer n, define an = n² sin +∞ 1. Determine if the sequence {an} converges or…

A: The solution is given below

Q: √1-(In x)2

A: ∫1-lnx2xlnxdx Let 1-lnx2=y

Q: Consider the function f(x) = 9 x³ Let F(x) be the antiderivative of f(x) with F(1) = 0. Then F(x) =

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Q: A producer of pedal-powered ice cream makers has determined that the revenue from the production and…

A: Given: Rx = 46x- 0.04x2 , 0≤x≤900 To find the interval of increasing and decreasing, we have to find…

Q: Find and sketch the domain of f(x,y)=√1-(x + 1)² - y² + 2ln(x -y + 1)

A: Let's find domain of given function.

Q: Thank you for your help! Also, what was the 3rd digit for the 4.04?

A: I think you need all answers having three decimal places. So,i am uploading all the answers with…

Q: The marginal revenue from the sale of x cans of air freshener is given by 4.4 -0.32√x dollars per…

A: In here, the marginal revenue is given as a function of x. So, we will use the formula: Marginal…

Q: Find the volume of a solid obtained by rotating the region enclosed by the graphs y = 19 - 2x, y =…

A: To find the volume of a solid obtained by rotating the region enclosed by the graphs y=19-2x, y=5,…

Q: Given the functions f(x)=√x² + 49 and g(x) = x4 fog would be equal to? O√x +49 O√x¹ +49 Ogof (x²…

A: The given functions are fx=x2+49 and gx=x4