I. Evaluate the following limits. sinh r2 → r2 1. lim z→0 sinhr 1

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Q: 1-) x ² ( xdx tydy) = (x² + y²) dx ; x =1 when y=2

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Q: 6. Find the area bounded by y= In x, y = 0 and x = e.

A: Area of a curve y=f(x) bounded by x=a, x=b is given by, A=∫abf(x)dx ln(e)=1, ln(1)=0

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Q: Find the equation of the family of curves having the given slope, and the equation of the curve of…

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Q: I. Determine the convergence of each of the following series using the indicated test. In number 4,…

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Q: (a) a) ₁₁ (x² +y) dy dx. Show all your work! 2 (b) ***1 1 dy dx. Show all your work! 0 2 ¹y² ff 1 dx…

A: SOLUTION-

Q: Use the Second Derivative Test to find all relative extrema. h(t) = -x + 6x² - 4

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Q: 6. csch x dx

A: To find the integral of the given function.

Q: 3. |2 – 2" | da - 22

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Q: Sketch and set up integrals for volume of the region bounded by y = x^2 + x - 2 and y = 3x + 13…

A: Please see the below pictures for detailed solution.

Q: Find the equation of the line tangent to y = e The equation of the line tangent is y= at x = 1 - In…

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

Q: -0.03t The function f(t) = 9000 e represents the rate of flow of money in dollars per year. Assume a…

A: The present value

Q: Q) choose one only 1) If y = (x − a)√2ax − x² + a² sin-¹(*), then y' = 2√/2ax-x² a a is constant. 2)…

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Q: 00 ermine the converges or diverges of the series n=1 = 1 (n+1

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Q: S 2sin(4x +9)dx

A: Given query is to find the integral.

Q: (Requires a short but nontrivial geometric Let ABC be a triangle argument.). with angles…

A: Using sine rule, length of other two side are evaluated.

Q: Perform the integration. 3 (13 (|3* − 1| + |3* − 3|) dx 0

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Q: Find the domain of the function of 5 log₂ (4-x²)+11 f(x) = 12x-31-2 + sin¯¹(1 − 2x) Express your…

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Q: Suppose that the number of crates of an agricultural product is given by 11xy-0.0002x² - 5y Z= 0.03x…

A: Suppose that the number of crates of an agricultural product is given by z=11xy-0.0002x2-5y0.03x+4y…

Q: y-coordinate of the centroid of the plane region bounded by 17 What is the the x-axis and the…

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Q: Given: zi = 2215° evaluate z and express the result in the Cartesian form. (Answer: j64)

A: Using De moivres theorem

Q: Annual sales (in millions of units) of a certain model of phone are expected to grow in accordance…

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Q: S 1 V1 + v 2

A: We have to find integral

Q: If (2, 1) is a critical point of f and fzz(2,1)ƒyy(2, 1) < [ƒzy(2, 1)]², then ƒ has a saddle point…

A: Here, the given statement is: If (2,1) is a critical point of f and fxx(2,1)fyy(2,1)&lt;fxy(2,1)2…

Q: C. Find the slope and the equation of the tangent line to the curve. 21: y=x²-4x+1 at (2, -3)

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Convert (z+ 2)² + y² = 4 to polar form. Drag and drop an answer to each box to correctly complete…

A: Let us assume x=r cos θ   and y=r sin θ. So, we get              (x+2)2+y2=4⇒(r cos θ+2)2+(r sin…

Q: EX 3! Show that F (x₁y) = (2xy - 3) + " + (2y + x² ) 5* is conservative and find a potential of it..

A: Use the partial derivative for finding the potential function

Q: Evaluate the following indefinite integrals. 1. [(5x + 4)¹¹ dx 2. √x (x² + 2)¹7 dx

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Q: 3. How much work does it take to pump the water in a full tank to 2 ft above the tank in the…

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Q: A real estate firm estimates that the value of a certain property will be given by the function 517…

A: To solve the following problem

Q: Evaluate fx² cosh x dx

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Q: Given cost and price (demand) functions C(q) = 110q+41,500 and p(q) = -1.9q+870, what is the…

A: Given  Cost function C(q) = 110q + 41,500  price function p(q) = -1.9q +870

Q: Problem 7. Find the limit lim f(x), where 2--2 x²-4 2+21 x-2

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Q: 4 -dx converges or diverges, and find the value if it converges. Determine whether the improper…

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Q: Set up the double integral that will find the volume of a solid bounded by z = 1- y²x² and the xy-…

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Q: (Requires a short but nontrivial geometric argument.). Let ABC be a triangle with angles…

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Q: 1. An open box is to be made from a 20-inch by 32-inch piece of cardboard by cutting out x-inch by…

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Q: Given Cost and Price (demand) functions C(q) = 120q+40000 and p(q) = -2.2q +800, what is the…

A: Given functions cost c(q)=120q+40000                             price p(q)=-2.2q+800…

Q: Solve the linear ODE using an Integrating Factor. dy dx - 3y = 8e5x

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Q: I. Determine the convergence of each of the following series using the indicated test. In number 4,…

A: The given series   ∑n=1∞(-1)nn+3

Q: A Consider triangle ABC drawn in a circle of radius 6 cm with vertex C at the centre of the circle,…

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Q: Find the area under the curve 4x2-3x+6 between x= -2 and x=3

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Q: (Requires a short but nontrivial geometric argument.). Let ABC be a triangle with angles…

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Q: First the pieces: End result (in terms of just t): dt 江 西 | Use the chain rule to find where 11 z =…

A: if z is function of x and y. Also x and y are of function t then derivative of z w.r.t "t"  is…

Q: (x² - 12x + 9) dx (x²-3x + 2)² 2. √(x²

A: Given: I=∫x2-12x+9x2-3x+22dx   As we know that; The Power Rule: ∫ax+bndx=ax+bn+1an+1+C And…

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Q: 1.) +y=e+ dx=3e-t 2. .) d- given: x(0) = 0, y(0) = 1 dy-x=0 d+y=1 given a z (0) = -1, y(0) = 1.

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Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -…

A: Given: Now,     v(t)=f'(t)      =-16t2+286t+10'       =-32t+286

Q: 5. Find the area bounded by y = sin √x and y = 0 on the interval [0, π²].

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