In th given equation as follows , approximate the function at the given value of x, using the polynomial found in the indicated exercise:- f (x) =ln x, f (2.1),

Q: Find the value a > 0 such that the tangent line to the graph of f(x) = x²e-2x at x = a passes…

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Q: Find an expression for the nth Maclaurin polynomial using sigma nota- tion for the function cosh x.

A: Suppose f has n derivatives at x=0 then nth Maclaurin polynomial of f is pn(x) where pn(x)=∑k=0n…

Q: 3 Given the function: f(x) = (1+ x)³/2 . x - 1 Prove that it is increasing on (0, +00) analytically,…

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Q: Let L(x) = ln(x² + 4x + 14) in the interval [-10,10]. What are the absolute extrema of L(x) in this…

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Q: Consider the function g(x)=5x2−18x+35. Find the area under the curve g(x) from x = -5 to x = 15 and…

A: Area under the curve  g(x) from x = –5 to x = 15

Q: (x*, where f(x) ={ 2, x> a 1. lim my x = a. x, x < a (where 'a' is last two digits of your student…

A: (1) We rewrite the function with given information as, f(x)=x2    x&gt;252      x=25x      x&lt;25…

Q: Proof the n + 1 derivative of xk is zero, where k <n

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Q: (a) Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x…

A: Consider the given piecewise function

Q: Q1 Let X1, .. ,X, f(r;0) = ()0 (1 – 0)2-, x = 0, 1,2. (i) Show that f(x:0) is a member of the…

A: It is an important part of statistics . It is widely used .

Q: For the given points X, = 1, x, = 1.5, x, = 2.5 and x, = 3. Find Lagrange Interpolation polynomial…

A: We have to find out Polynomial using given values and function.

Q: Given a function f with input that has the dimension [x] = L-M-T-1, such that [f(x)] = L-M, find the…

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Q: In deriving the three point formulas, we use Lagrange polynomial. L o(x) at x = xo is (notice the…

A: Note that, the formula for L0'x in deriving the three point formula is…

Q: In deriving three point formulas, we use Lagrange polynomial. The derivative of L, at x, is: Select…

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Q: (B) Verify the Mean Value Theorem for f(x) = ln(4x + 1) on | 0,

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Q: Let f(x) = x ln(1+ x*). For all æ € [-1, 1], it is known that In(1 + x) = (-1)" -xn+1 n +1 n=0 2.…

A: Substitute x3 for x in the given power series of ln1+x and simplify.…

Q: Given f(x) = ln(x² – 2x + 5), over the interval [ – 2, 3], answer the following: a) The point where…

A: Given, f(x) = ln(x2 -2x +5)            x∈[-2,3] f'(x) =2x-2x2- 2x +5  and f''(x) = 2(x2 -2x +5)…

Q: Q1 Let X1,. , X, f(r;8) = ()0"(1 – 8)²-²,x = 0, 1, 2. (i) Show that f(x;0) is a member of the…

A: It is an important part of statistics . It is widely used .

Q: Let f(x) be defined by f(x) = x − 2 ln(x), for x > 0 Part a: On what intervals (if any) is this…

A: For increasing f'(x)&gt;0

Q: Consider ey²cosxy – log3xz = e*z implicitly defines z as a function of x and y . Find and using…

A: The given function is: eyz cos(xy)-log3(xz)=exz

Q: Can you help with this problem step by step?

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Q: f(x)=ln(1+x/1-x) is function even or odd

A: We have to find the given function is either even or odd: fx=ln1+x1-x We know that for even function…

Q: Let f(x) = loge (3 + x)   a) Find f n)(x) ; the nth derivative of f(x) b) Using Taylor's theorem,…

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Q: 2. For the given functions f (x), let.x, = 1,x, = 1.25, and.x, = 1.6. Construct interpolation…

A: Step:- 1 Lagrange Interpolating polynomial:- P(x)=f0 L0(x) +f1 L1(x)+ f2 L3(x)+....fn Ln(x),Here,…

Q: If f(x)=ln(x) and x,-3.1, x₁-3.2, x-3.16, then the error bound in Lagrange interpolating polynomial…

A: Given the function is fx=lnx and x0=3.1, x1=3.2, x=3.16

Q: find the extreme values on the interval f (x) = x − 12 ln x, [5, 40]

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Q: Jsing only exponential (e*), cubic (x³), and the cosine (cos x) functions, create anot unction for…

A: To find: A function using the given functions for which the derivative computation requires using…

Q: Fit a second order Newton's interpolating polynomial to estimate log 10 a) Interpolate using xo =…

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Q: Let g (x, y) = 7 sin(xy) — 9x² ln(y) + 8. Find the degree 2 polynomial, p, which best approximates g…

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Q: 55. By normalizing the function f(x)==-defined in the domain [0, 2], we will get as a result the…

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Q: Given a surjective function f: [-1, 1] → [-1, 1], prove or disprove: f-(f{}) = {0}. Find f(E) and…

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Q: Fit a second order Newton's interpolating polynomial to estimate log 10 a) Interpolate using x, = 8,…

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Q: The derivative of f(z) = Log(2iz – 4 + 6i) at z = -3 + 4i is Log(-12). Undefined. 2i -12 None of…

A: Derivative of function f(z)=Log(g(z)) where g(z) is some complex function. f'(z)=g'(z)g(z)…

Q: 2 2x +1 Let f(x) =- |- log, (x² + + 1) • (b* - 5b +3)x +c. If f(x)isa tan decreasing function of x…

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Q: 8. Find the derivative of the f(x) = ntan x at x = " А. п B. 2 In(1) C. π In (π) D. 2 n In() E. 2n…

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Q: Find the polynomial f(x) of degree 6, 1/x which satisfies lim{1+ f(x)] =e? x3 X-0 and has local…

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Q: Q7: Use the MEAN-VALUE-THEOREM to show that x-1<e* < 2x+1, 0<x<ln 2.

A: Since you have asked multiple question, we will solve the first question for you as per our…

Q: Find derivative of the following function by using formula f(x)= limit _f(a) - f(x) а -х a→X (3х-1)…

A: To find:

Q: Prove that if the (n + 1) th derivative of a polynomial vanishes but the nth does not, then the…

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Q: Find the linearization at x = a. f(x) = sin3 (x), a = 4 (Use symbolic notation and fractions where…

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Q: Find the minimal polynomial that will approximate the function F(x) with an error of magnitude e <…

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Q: Q2 Let X1, .. , X, * f(r;0) = že¬=/°, r > 0. %3D (i) Show that f(x;0) is a member of the exponential…

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Q: Let k be a fixed positive integer. The nth derivative of 1/(xk − 1) has the form Pn(x)/(xk − 1)n+1…

A: Given: nth derivative of 1xk-1=Pnxxk-1n+1 Find: Pn1

Q: If f(x) = x2+1 for x > or equal to 0, then is arcf(x) has a tangent at x=1

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Q: Let g (x, y) ) = 11 sin(xy) — 13x² ln(y) + 20. Find the degree 2 polynomial, p, which best…

A: Given: The function is g(x,y)=11sin(xy)-13x2ln(y)+20 To find: The degree 2 polynomial which best…

Q: 3. If G(x) = tan x, find G(rt/6), G(x - T/2), G(-x) and express G(2x) as function of G(x). 4. If…

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Q: a) Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x…

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Q: Let g (x, y) = 9 sin(xy) – 11x² In(y) + 4. Find the degree 2 polynomial, p, which best approximates…

A: Given: g(x, y) = 9sin(xy) -11x²ln(y) +4 To find: Taylor Polynomial of 2nd degree   Dear student,…

Q: Q) Find an approximation to one of the zeros of p(x)=x 3-2x2-5 using Newton's method and synthetic…

A: Given px=x3-2x2-5

Q: A. Compute the bound B of the error when approximating f(x)=sin(x) with a polynomial of degree 1 in…

A: The given function is fx=sin x. Find the error bound for f approximating with a polynomial of degree…