Q1. Use the Fundamental Theorem Of Calculus and the Newton-Leibnitz rule to answer the following: 1. Determine cln(x) tan(vt)dt. d dx 2. Calculate 10 In xdx.

Q: 1 4. First, make a substitution and then use integration by parts to evaluate [Hint: Use the fact…

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Q: dw Find the value of- dt at the point (1, In 2 ,0) on the curve x = cos t ,y= sin t, 0 <t< 2n where…

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Q: Apply the Fundamental Theorem of Calculus to get the following derivative. d. In( t?+1) dt dx 1

A: Given, fx=ddx∫1x3lnt2+1dt To Find: f(x) by applying fundamental theorem of calculus.

Q: Apply the Fundamental Theorem of Calculus to get the following derivative. d In (t² + 1) dt dx 1

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Q: Find d2x/dt? as a function of x if d 6x sin x. dt? ||

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Q: tan x dt+ 1+ t? (1+ f')* 1 -dt=D1 1/e Ve prove LHSis equal t RHS

A: This question is related to integration. We solve this question we divide this question in two part…

Q: Prove that sinh−1 t = ln(t + √t2 + 1 ).

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Q: The velocity of a particle moving back and forth on a line isy = ds/dt = 6 sin 2t m/sec for all t.…

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Q: Differentiate g(t) = (at + 1)2 with respect to t. Assume that a is a positive constant. g'(t) =

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Q: 10. Use differentials to estimate to estimate sin(46°). vZ(n+180) А. D. VZ(T+180) 360 180 В.…

A: Let y = sin (x)

Q: Use the modified Euler Method to solve the ODE = subject to y 1 when x 0 %3D dx 1+x on the interval…

A: To find y(0.3) by using the modified Euler's method.

Q: 3. (4 pts) Find the exact value of each definite integral. 4x5 dx (b) dt

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Q: Calculate the following definite integrals. -1/2 1 dx "dx dt (t+2)³

A: As per the company guidelines we can solve first three parts. I hope that the given solution will…

Q: Calculate the derivative e10x de L9 In (t)dt using Part 2 of the Fundamental Theorem of Calculus.…

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Q: Find G(1), G'(0), and G'(π/4), where G(x) =

A: Here we have;  G(x)=∫1xtant dt

Q: 2m 28. t sin 2t dt

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Q: Given Lve f(t) dt = In(x) cos(x) + sin(3) :L.e- f(t) dt, find f(x). sin(3)

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Q: Evaluate lim X→0+ dx d sin ť dt . t O a) 1 O b) 1 c) 0 d) None of these e) H/2 5/2

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Q: F(x) = sin t dt, [0,1] 0. F(x)]

A: The following formula for Maclaurin's series expansion of sin x will be used: sin x=x-x33!+x55!-...…

Q: Use Part 2 of the Fundamental Theorem of Calculus to find th. derivatives. dt sin y dy 1+ y? (b) dx…

A: Consider the integral ∫axfydy, where a is a constant. Note that, ∫axfydy will be a function in x.…

Q: d Use the Fundamental Theorem of Calculus to find the derivative. dx dt 1+ vE

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Q: Use the Newton-Rhapson method to estimate the root of f(x)= ex -x employing xo=0. E = 0.1%

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Q: For the functions w = 8x + 3y, x= cos t, and y = sin t, express dw as a function of t, both by using…

A: The given function is w=8x2+3y2, x=cost and y=sint. We have to express dwdt as a function of t.…

Q: 1. Use the Fundamental Theorem of Calculus to evaluate the following (DO NO 5x -6x dx 1 | cos (x)--…

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Q: Use at least two methods to prove that dr/dt=0 when r=√x2 + y2, x=α cos t, and y=α sin t if α is a…

A: First method   r=x2+y2r=(α cost)2+α sint2            since x=α cost and y=α sint  =α2cos2t+α2sin2t…

Q: If f (x)= [a(«) =os* '(5) [1+ sin(t?)] dt find f 1 dt, where g(x) V1+t3 COS X

A: We need to find value of derivative.

Q: Evaluate the integrals

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find dw/ dt at the given value for the following functio 1) w=x² + y°, x = cos(1), y = sin(t), at †…

A: The given functions are w=x2+y2, x= cost  and  y=sint and t=π. Evaluate w in terms of t as follows.…

Q: The tangent line to the curve y=f(x) is horizontal at where X = Xo f f(xx) = 00 A O f(xo) = 00 .8 O…

A: The tangent line to the curve y=f(x) is horizontal at where x=x0 if

Q: d rx Cos t dt dx J-x Vt2+1

A: Definition used -                 The first fundamental theorem of calculus -…

Q: Use the Fundamental Theorem of Calculus to calculate the following derivatives: 4 d (a) d.r cos(4t²)…

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Q: Express in the form x + jy (3) sin(t/4+j2)

A: Complex Number Question

Q: In (6x) to x if y = sin (5e') dt.

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Q: Assume that z and y are both differentiable functions of t and are related by the equation = cos…

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Q: Use the method of first principles to show that d/dt(lnt)=1/t

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Q: Evaluate: L{t f -t e2t Cos t dt}.

A: Evaluate: Lt∫0te2t costtdt First of all we find    L(cost)=ss2+1L(e2tcost) =…

Q: Given z = sin(1 - 2). x = 2 – ts and y = 2t – s - then calculate when t = -1 and s = -1. dt

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Q: 2s Prove that L(t sin t) (s²+1)²

A: We can use the concept of Laplace transform in order to solve the given problem.

Q: The linear approximation at x = 0 to sin(4x) is A + Bx where A is: and where B is:

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Q: Q1. Use the Fundamental Theorem Of Calculus and the Newton-Leibnitz rule to answer the following: 1.…

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Q: Use Part 2 of the Fundamental Theorem of Calculus to find the derivatives. d/dx ∫_0^x▒〖e^√t dt〗…

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Q: 10. Find the indefinite integral. Te cos 3t dt dv u = du = v =

A: Given integration is : ∫e9tcos3t dt   To find the value of integration.

Q: If x = 3 sin* t and y = 2 cos" t , then find dy at t = dx 4

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Q: Q1. Use the Fundamental Theorem Of Calculus and the Newton-Leibnitz rule to answer the following: 1.…

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Q: (e) S x³ cos(x²)dt (hint: use substitution first) VT/2 COS

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Q: Consider the following. dt (4 + t? Let t = 2 tan(0) and determine the following. 2 sec-(0) dt = de t…

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Q: If r = sin (ƒ(t)), ƒ(0) = pai/3, and ƒ′(0) = 4, then what is dr/dt at t = 0

A: Given:

Q: 15 Evaluate the integral (10 + sin t)" cos t dt using the substitution u = 10+ sin t. + sin t) cos t…

A: We are asked to evaluate the integral.

Q: Q2: find dw/dt at given value point for the following function x= cos°(1), y = sin²(1).= =-. 1 at t…

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Q: Using Part I of the Fundamental Theorem of Calculus, 8 d evaluate: dx t7 dt =

A: Given that ddx∫x8t7dt