Find the limit. lim tanh(x)

Q: Find the derivative of the function. f(x) = In(sinh(x)) f '(x) =

A: f(x) = ln(sinh(x)) here we use chain rule f'(x) = cosh(x)/sinh(x) f'(x) = cot(h(x))

Q: Use Green's theorem to evaluate F. dr. (Check the orientation of the curve before applying the…

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Q: Consider the lines defined by the equations (3 : z – 3 = y – 5 = z – 6 and l4(s) = (-2 – 2s, –2s, 6…

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Q: Sinx /2

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Q: Find the length of the spiral r = 80 for 0 < 0 < 3. (Use symbolic notation and fractions where…

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Q: sin x dx 1- sin2 x 4. cos x dx 2+3 sin x 5.

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Q: A wooden rectangular box is to be made of lumber that is 2/3 in. thick. The inside length is to be 6…

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Q: x'+8 if x + 2 The function f given by f(x) = is continuos at x = -2 x+2 -12 if x = 2

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Q: 5. Let f be a function satisfying the following properties: continuous on R \ {0} • f(-1) = -3 •…

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Q: a) lim 3x + x2 x→1

A: We are asked to find the limit.

Q: x² – 1 lim x→1 /x – 1

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Q: (x² -2x9 dy Solve The firest orler oDe

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Q: (xcosx + sinx) dx + -sinx + 6 )dy y = 0;x=0;y=1 |

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Q: Convert the polar coordinates (3, 2) to Cartesian coordinates. (3, 0) (0, 3)

A: Given: (3,2)

Q: 4) For each graph in Figure 16, determine whether f' (1) is larger or smaller than the slope of the…

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Q: 1 1. X CasCx y) dxdy. 0.

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Q: What is the slope of the line 0 = (Use decimal notation. Give your answer to three decimal places.)…

A: Slope of a line θ=a is given by m= tan(θ)=tan(a)

Q: Show that the following are equal using set identities. Provide the correct solution with the name…

A: The left side is: C∩C-B∩C∪A∩B-B∩C-A We first simplify inner parts:  C-B∩C A∩B-B∩C

Q: |sin(x)cos(2x)sin(3x) dx sin(3x)cos(3x), sin(2x)cos(2x) sin(2x) 12 8 8. + C 4 sin(6x) sin(2x),…

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Q: S, f(2)dx+ f(x)dx = 21. 23. S f(G)dr + J, f(x)dx =, = <p(x)f f – xP(1)f !!

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Q: (7) If 4.5* = 97, an approximate value of x is (A)x = log(97) × 1.987 (C) x = In(97) z 4.575 (B)x =…

A: 7.    4.5x=97 Note:      Multiple questions are given, we are answer with only one question. if you…

Q: dy Find for the curve: x dx :4 cos t, y = 16 sin t, 0<t < 2T

A: We have to find dy/dx for the given function

Q: Activity 2. Using U Integral of the following. 1. S sec?x dx 2. S Substitution or Integration by…

A: As per bartleby guidelines we only give first question answers.

Q: To evaluate dx using trigonometric substitution, which of the following is the new integral form in…

A: Given integral is ∫x2-x2-1 dx.

Q: all

A: We have to find the following conditions according to the given graph of the function

Q: Q.3 - Evaluate |sec xtan.x dx.

A: As we know that ∫sextanxdx=secx+Cand dsecxdx=sectanx

Q: 3.12 Еxpress lim n00 n k3D cos 1+ as an integral. (Be sure to include the lower and upper limits|of…

A: Given: limn→∞ 2n∑k=1ncos1+2kn To convert this into the integral , use the following method

Q: 6. A bax with a square base is to have an open top. If the lateral surface of the bax is 100 cm",…

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Q: Find the most general antiderivative or indefinite integral. 14 5x Зх+ 2) dx -3x+ 14 5x -3x+2) dx% =

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Q: Complete the table shown to the right for the​ half-life of a certain radioactive substance. ​…

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Q: x arcsec x dx ? xdx A. x Arcsec x - 25- ... B. ** Arcsec x -- V-1 xdx xdx C. x Arcsec x + 25- xdx D.…

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Q: Find an equation for the tangent line to the curve at the given point. Then sketch the curve and the…

A: Given: y=8x, 16,32

Q: Using Integration By Parts ∫ 2x^2 e^(1/3)x dx find uv - ∫ v du

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Q: Find the polar equation of the line y = 7x + 5 in terms of r and 0. (Use symbolic notation and…

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Q: Let C be the parametric curve defined by x(t) = t² – t – 2, 1 y(t) = t3 – t2. 2 %3D (-:) 3 -2,…

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Q: Integral 1.

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Q: an onine SOcial group nad 3o0 miion Tme uently, new me m(t) = -3.3t2 + 14t + 230 million members per…

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Q: V5 +3 v3 - E-2 where k is an integer to be found. V5 + V3 Without using a calculator, show that Cs…

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Q: Express the polar coordinates (-2, -7) as Cartesian coordinates. (2, 0) (0, -2) O (0, 2)

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Q: Consider -(x Using a suitable trigonometric substitution, the resulting integral in terms of 0 is…

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Q: Find the particular aolution of the differential equation with the initial condition given below.…

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Q: ta the téduction of order melhod, the substitution y= 5u can be used for the DE: - 3y/= 0, to obtain…

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Q: 3 // 7xyz² dxdydz ? What is the value of the integral 0. Select one: O 133/4 O 135/4 O 137/4 O 139/4…

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Q: 6) A 13 ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate…

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Q: Decide which of the following regions has n () in area = lim tan 2n 2n i=1 without evaluating the…

A: To decide which of the regions has the given area.

Q: 4. S Vä(x² + 2) dx 5. S(-3 Vã – 6x v7) dx 6. (9x*-6x²+7x²-5x+15 dx 3x

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Q: integral

A: We have to choose the correct option from the given options according to the given information

Q: Point U is on the curve y = ln(x). Let O be the line joining U to the origin. Find the coordinates…

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Q: w +x +4y +3z =5 2w +3x +y-z =1 w +2x -5y +4z = 3 w -3z =9

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Q: Solve the differential equation y tana+y = 3 sin r. %3D sin I A sin a B sin r + C Cos a c - sin I +…

A: We have to solve the differential equation: y'tanx+y=3sinx