1. Let f(x)=sin(x) and apply theorem(4.1) a. Use xo-0 and find Ps(x), P-(x), and Po(x). b.Show that if |x|<1 then the approximation sin(x) x - 3! 5! 7! 9! has the error bound TE,(x)| < ÷s 2.755 74 × 10-7. 10! c.Use xo = and find P5(x), which involves powers of (x-). %3D

Q: (a) Is Rolle's Theorem applies for the function ƒ(x) = cos(sin¬'x) on the closed interval [-1, 1]?…

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Q: 0 T/2 f(x) | 1 X -1

A: Solution-

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Q: 5. Find the absolute maximum and minimum of f(x) = 3 cos x on the interval [0, 27).

A: 5) to get critical points f'(x)=0f'(x)=ddx(3cosx)=-3sin(x)=0…

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Q: 2.) Consider f(x) = sin2x for xo = 0, x₁ = 0.25, x2 = 0.5, x3 = 0.75, x4 = 1.0. Calculate f2' using…

A: Given that  fx=sin2x and x0=0, x1=0.25, x2=0.5, x3=0.75, x4=1 and h=0.2, 0.02

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Q: 6. Find all the values of z satisfying sinh z = = -j1.

A: What is Hyperbolic Function: The hyperbolic functions in mathematics are comparable to the…

Q: 1. Find the critical numbers of f(x) = 2 cos(r) + sin (x) %3D

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Q: 1 Find Maclaurin polynomial P, to f (x )= : 1 1 cosx sin Ax 1-x 1+x

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Q: 2. Verify that the Mean Value Theorem (MVT) applies to the function f(z) = sin² z- on the interval ,…

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Q: Consider the function f(x) = cos x − 3x + 1. Since f (0)ƒ () < < 0, f(x) has a root in [o,]. If we…

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Q: 1. Show that f(x)= 4 sin(44)+2-x has at least one zero on (-1,0J. %3D

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Q: Thus, for u = g(x) = sin(5x), %3! f'(g(x)) = F'(sin(5x)) = 8 %3D %3D 8 Next we calculate g'(x). g(x)…

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Q: 23 Given f(x) = +1, that is defined over [1, 6]with a step (h= %3D 2+ sin(x) 1). Using the divided…

A: Given that, f(x)=2x32+sinπx+1 The NGF formula is, P2(x)=y0+q∆y0+q(q-1)2∆2y0 Where q=x-x0h Here…

Q: 10. Find all the values of a in the interval [0, 27] such that f (a,=) - fxx (a,=) = 0 for f(x,y) =…

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Q: 5) Give a big-Oh estimate, 0(x³), for the function f(x) = (1+ 2x + 2cos x + 2x2)(log x² + 3|x| + sin…

A: 5 Given that the function is fx=1+2x+2cosx+2x2logx2+3x+sinx+cosx......1. We have to estimate Ox3 and…

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Q: 1+ x² -L „tanx - for all x €[0,1/2], then f'(x) equals 1+ ex * If f(x) = sec2x A 1+ etanx sec³x B 1+…

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Q: 13. ebx cos x dx exists only when b < 0. lim t→∞

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Q: If f(x,y,z)=In(x²y+sin?(x+y))+111x112y2z113, then at (1,1,1) is equal to əx²əyəz

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Q: 25. If f(x) = (cos x)*, then %3D is k-0

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Q: Express T(x)sin x-root(3)cos x into the form of T(x)=Asin(x+theta) , where A>0

A: Sin(A+B)=sinAcosB + cosAsinB

Q: 1 Find Maclaurin polynomial P, to ƒ (x )= 1 1 sin Ax cosx 1-x 1+x

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Q: Find the critical numbers of the following functions. a. f ( x ) = 2 cos x + sin 2 x b. f ( x ) =…

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Q: Find any critical numbers of the given functions 1. f(x) = x* – 4x² 2. g(x) = 4x x2+1 3. h(x) =…

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Q: 5 find aroot of the eqution f(x)=x²-4 Sinx = 0 using the 2 Newton-Raphson, Xo = 3,6=0.0005

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.