S (2t)*dt lim x→ =? х* — 1

Q: y(x) = tan{/3x² + In(5x*) - In(5x'

A: Given  y(x) = tan3x23 + ln5x4 We have to find dydx.

Q: Determine if the improper integral converges or diverges: 1 dx. 1+x²

A: Our Aim is to determine whether the improper integral given below converges or diverges∫0∞11+x2 -(i)

Q: Q2 find the derivative of the following: 1) y = 2stn²(5x) ,2) y = Inx'n cosh 5x ,3) xsin¬14y = y…

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Q: dx (x– 1)%

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Q: (b) Find the value of the improper integral dx with infinite interval of integration, if they…

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Q: 3) Estimate Y(2) using Euler's method with 0.5 long dY intervals. Y - 2X and Y(1) = 0. dx

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Q: Compute dy/dx for the function. y = sinh 2 8x O 2 sinh 8x cosh 8x O 2 cosh 8x 16 sinh 8x cosh 8x 16…

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Q: Express the limit as a definite integral. n 7 lim 2 3x Ax: [2,7] Ax,0 k= 1 O A. 3x' dx 2 о в. 3x'd…

A: We have to express the given series as a definite integral.

Q: 4. Indicate if each improper integral converges or diverges. a) ['te*dt dx c) Lo1+x -2t а) b) x -1…

A: The given integrals are: a) te-2t limit from 0 to infinity.  b) x/(x2-1) limit from 3 to infinity.…

Q: Determine whether the improper integral diverges or converges. dx 1.f (2x-1)³

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Q: Express the limit as a definite integral on the given interva lim [2(xf)³ – 5x¡]Ax, [2, 5] n- 00 i =…

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Q: Determine whether the improper integral diverges or converges. dx 1. (2x-1)3 7 dx 2. -1* + 1

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Q: If the integral diverges, indicate that using the checkbox. 6 dx The integral diverges x(x + 1)

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Q: find dx/dt at x=1 if y=3x^2+3 and dy/dt=1

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Q: Find dy/dt when x = 1 if y = x2 + 7x - 5 and dx/dt = 1/3.

A: Given:

Q: At time t = 0, then th

A: P(t)=0.5t4-16t3+144t2       , 0≤t≤12At t=0 the sale begins,costco is having a 12 hour sale,The rate…

Q: •4 x dx 10 x2 – 9

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Q: Find the derivative. (Hint: en a = x) %3D y =S 4 In x et dt O * - 1 4x3

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Q: 10. Determine whether the improper integral converges or diverges 3 dx (x – 1)3 -

A: Given query is to integral converges or diverges.

Q: Express the limit as a definite integral on the given interval. lim [4 – 3(x¡*)² + 6(x¡*)>] Ax, [0,…

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Q: 8) Find the linearization of f(x) = 6 + X+1 tan 4 dt at x = 0. 1.

A: On solving this we will get

Q: Express the limit as a definite integral on the given interval. lim (2-5(x,)² + 6(x;")³] Ax, [0, 4]…

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Q: 2 1 Estimate -dx using the right endpoint rule with n = 4 3 1+x

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Q: Suppose y = square root 2x + 1 where x and y function of t . A) if dx/dt =12 , find dy/dt. When x= 4…

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Q: If f(x) = Α) B C D tanx sec ³x 1 + e tanx 1+tan²x 1+ e tanx sec²x 1+1² 1+e' -dt, then f'(x) equals…

A: We have to find derivative of given integral.

Q: dx 4. Determine if the integral converges or diverges. (x – 2)

A: In this question we have determine the integral converges or diverges

Q: 4. Find the differentiation dy. using definition with limit of the following: y = V2x + 1.

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Q: psen(x) tan(t) dt lim ctan(x) Vsen(t) dt x→0

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Q: Determine if the integral converges or diverges by comparison.

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Q: Express the limit as a definite integral on the given interval. cos(x) Дх, [2л, Зл] X; lim Зл dx 27

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Q: Show if x, is convergent or divergent T.3 'n sin(x) dx 1+x S'

A: Introduction: The convergence or divergence of an infinite series depends upon the sum of the…

Q: 2. Given that y= -- Use a limit to find the instantaneous rate of change of y with respect to x at…

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Q: at x sin- 1 lim e J1 x→1 In x " 2 dt =?

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Q: Find dy ify Yify = sın 2x. dx

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Q: arctan(x) dx 2 + ex 20 Jo convergent divergent

A: Answer is convergent.

Q: 1 dx is convergent x" If n>2, the integration

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Q: fil experini for dy txďn

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Q: .2 x+15 dx Jx* +3 1

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Q: 1 Determine the convergence of the integral | dx. (2 – x)

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Q: Find dy dy dt at x = z - 1 if y = -5x² + 3 and dx dt 5.

A: topic:- derivatives

Q: 55. Show that dx J+4 converges by comparing with x³ + xdx. -3 dx. х

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Q: Find dy ax oy Impticit dipTErentation 3. Find 2nd derivative

A: 1) The given equation is 2x2+2y2=17 Differentiate both sides of given equation 2x2+2y2=17 with…

Q: Use the First Fundamental Theorem of Calculus to find F"(x) if = [*_ sinh√/1 +ť² dt. F(x) =

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Q: show that the lim dose not exist x.y-00

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Q: Limit 0 to 2 √x dx

A: We have to find the definite integration: ∫02xdx We know the formula of integration, ∫xndx=xn+1n+1+C…

Q: 2. ху 4 a. when x=8 10 dx b. when x-1 dt dy dt -6

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Q: Does fn converges to L1 and L2 i.e the distance between fn and f goes to 0

A: By the theorem: A metric  on BE is the uniform metric du  . A sequence of bounded functions fn:E→ℝ…

Q: tan Зy limy 0 3y O 3 O undefined

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Let x > 0 and b > 0. Show that

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Q: Compute the following. (a) limz-2i (2z+3)(z-1) z2 – 2z+4 (b) Derivative of (1 – 22)*. - IT/4 (c) S7…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.