Question 1: Let f(x) = In(x? +x + 1), x € [-1,-5. Find (if any exists) B) min, f(x). C) sup f(x). inf, f(x) А) max, f(x). xej-1 D) zel-1,

Q: 1 Let f (x,y) =In Then f (1, – 1) =... 3x2+4y3 XX

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Q: 1. A natural cubic spline S.on [0,2] is defined by (S.(x) S(x) = {x)=1+ 2x-x s,(x) = a+ b(x- 1) +…

A: The cubic spline is defined as: Sx=S0x=1+2x-x3 if 0≤x≤1S1x=a+bx-1+cx-12+dx-13 if 1≤x≤2 From…

Q: Section 1.5 In Exercises 1 and 2, we refer to a function f, but we do not provide its formula.…

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Q: Question 4: Consider the function (kt+1) = kt+1, where St = S(rt+1) = S(r(kt+1)). St Differentiate…

A: Given- Consider the function Ωkt+1 ≡ kt+1st, where st = srt+1 = srkt+1.  To find- Differentiate the…

Q: 1. Let f(x, y) = In(x - y) then at the point (4,1), fryis equal to: %3D -1/9 O 1/7 1/9

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Q: =: (1)6 In(t)dt, 1, = e.

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Q: 22 dt at x = 4. ind the linearization of f(x) = 7 - 4 +t

A: Consider the given function fx=7-∫7x+3224+tdt

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A: Given equation is Differentiating both sides, we get Now, we will wind critical points of f(t) in…

Q: 2. Determine whether the functions f1(x) = e2", f2(x) = e=2#, and f3(x) = sinh 2x are linearly…

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Q: 3. (a) Show all functions satisfying u"(x) = 0 are linear by integrating the expression of u"(x) %3D…

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Q: 1 Prove the inequality: EP, log(-)<P, log(- P i=1 i=1 N N with the constraint: EP, =EQ, = 1 i=1 i=1…

A: The given constraint is  ∑Pii=1N=∑Qi=1i=1N To prove that ∑n=1NPi log 1Pi≤∑n=1NPi log 1Qi

Q: *18. (section 3.4 ex 3.) Prove that if f(r) is continuous and f(z) = S() dt, then f(x) is…

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Q: 2x* + ax + b Part A: Consider the function f defined over]-0; 2[ U]2;+«[ as : f (x)= where a x- 2…

A: Given data: The given function is f(x)=(2x2+ax+b)/(x-2). (a) The expression for the derivative of…

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A: we have to swap variable for finding the inverse function

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Q: ¸(1+ h)² −1 lim h→0 h using the squeeze Theor

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Q: 5. Determine a function v(r, 0, ø) with Av = 0 _in B2 \ B1 satisfying the boundary conditions v(1,0,…

A: Use the cylindrical coordinates to determine the value of r. Now use the boundary conditions to…

Q: Theorem 17-1. If T, is a consistent estimator of y(0) and y {y(0)} is a continuous function of y(0),…

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Q: (a) Let f(r, y) = -2r*y² – In(y²). Compute fyzz (b) Let g(r, y, 2) = 1(3y* – 52²). Compute

A: (a) Given function is fx,y=−2x5y2−lny2 We have to find the fyxx. First differentiate…

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A: Given the statement

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Q: (a) Express the initial value problem: 1 s'(x) = -f(x), for x +1 f(0) = 1, as an integral equation…

A: The Initial value problem is given as, f'x=-1x+1fx, for  -13≤x≤12                         (1) with…

Q: prove that F(r) = 4z-3z is chaotic on the interval [-1,1]. (Hint: consider g(6) = 30 on S'.)

A: The given function: F(x)=4x3-3x The given interval is [-1,1] To prove that F(x) is chaotic: Chaotic…

Q: (a) Show whether if 0<x <1, f(x) = 2 - x if 1<x < 2 is a Dirichlet function.

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Q: f(x) = 3 x4-4 x3 -12 x2+1, has local minimum at x = OA. OB 2- OC. OD.

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Q: The Wronskian 1. Show that the functions e", cos x and sin x are linearly independent. 2. Show that…

A: 1. The functions ex, cos x and sin x are linearly independent.2. The functions 1, sin2x and cos2x…

Q: Example 1.7.3 Prove that dx/x is divergent. 1

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Q: a) Exaluate: %3D :(?)6 puo (x puif (9 and (3 +x x <O %3D for which f (x)=9). Give exact working out…

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Q: 1. Determine whether the functions f1(x) = cos 3x, f2(x) = x, and f3(x) = cos² x are linearly…

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Q: 2.2 11, IfF = xyz\+x*y°z}+ xyz k then find div F at (2, 1, – 3).

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Q: 22. 13: Fundamental Theorem of Calculus y(x) : V1- t2 dt Find g'(x). Answer:-

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Q: 1.4 For which values of a eR is the function ar? f(x + iy) = (a'x – axy) +i (- + ay an entire…

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Q: 4.8. Show that Dirichlet's function 1, if x is a rational number, { otherwise f(x) = 0, is not of a…

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Q: Find the minimum and maximum of A over a particular interval [0, 6]. A(x) f(t) dt The graph of y =…

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Q: 2-3. If f is integrable on [a, b], then ("f(x) dx = lim E f(x) Ax i=1 • In the theorem above, define…

A: We know that integration is equivalent to summation as mentioned above. Here, △x is the small step…

Q: 1 Let f (x,y)=In . Then f „(1, – 1) =...... 3x²+4y3 XX

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Q: (c) Apply the golden ratio search method to locate the minimum of the function f(x) = 4x³ – 20x +…

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Q: 26: Let X B(3,0) that is f(r; 8) C)0* . (1 – 0)3-,1 0, 1,2,3;0 < 0 < 1. %3D Let Ho 0 and H 0 =!.…

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Q: Pracbte 111 co° exist, which statement is most likely true? If the function f(x) has a local minimum…

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Q: 3)if f(2)=1/z, has zero of order mat z=0, then f(z) has a zero of order m at d) e a) ∞⁰ b) 0 c) 2in²

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Q: and y-f a. Let =-5 Find the veetoes d %3D %3D

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Q: 5.2-9. Determine the constant c such that f(x) cx (1 – x)°, 0 < x < 1, is a pdf. |-

A: Given: fx=cx3×1-x6        0&lt;x&lt;1

Q: Question * A natural cubic spline S(x), for a function f (x) is defined by x2 ax3 4 2' 1<x< 2 3 S(x)…

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Q: 1. independent in the interval I=(-5, 10)? Are the functions y₁ (r) = max(0, z), 32=1 min{0, z), and…

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Q: f(x) = 3 x4-4 x3-12 x2+1, has local minimum at x= 1 40 2.80 .CO .DO 0.

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