Prove that P (a

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

A:

Q: Let P(x) = tln(t) dt. Use part 1 of the fundamental theorem of calculus to determine if P(x) is…

A: Given function is

Q: 13. If f(x) = 1 / (5 + 7x) , find S f(x) by using a u-substitution. Show the u-substitutions.

A: Given, fx = 15 +7x  We have to find ∫fx using u substitution

Q: Find the funchion f Such that F(x) xf (x)-x and fo) 2

A: Convert the given problem to a simple differential equation and solve the same.

Q: Show that f(r) = O(|x – xo|*) and g(x) = o(]x – roP) imply f. g(x) = o(|x – xo]k+i). - -

A:

Q: Find conditions on a and b that ensure f (x) = x3 + ax + b is increasing on (−∞,∞).

A: Consider the given function as fx=x3+ax+b

Q: 3. Let f(x) = x, given the interval [0,1]

A: fx=x, x∈0,1 f'x=1>0 for all x∈0,1 So, fx is strictly increasing on the interval 0,1.

Q: Find a value c that verifies the conclusion of the Mean Value Theorem for the function f(x) = x² on…

A:

Q: Let g=yf(xy). Show that: - дд у ду дд - Х = g дх -

A:

Q: 2. Let f(x) = S dt for x 2 2 In a) Find F'(x). b) Is F increasing or decreasing? What can you say…

A:

Q: Find all a E Z such that f(x) =

A:

Q: 1 Let f(x) = 8 + In (t) dt, for x2 1. Find f'(2).

A:

Q: 2. Find the linearization L(x) of f(x) = x³ - 2x + 3 at x = 2 and use it to approximate f(1.9) and…

A:

Q: 8. Consider the function f(x)=/25-x² . a. Find the linearization L(x) of f(x) at x=3.

A: Given expression is , fx=25-x2 to find out the linearization L(x) of f(x) at x=3.

Q: 1. Find of ахду OF f(x,y) = xy (x+y-1) -x2

A:

Q: If 0 < f(x) < g(x) for all x and I f(x)dx diverges, then | g(x)dx diverges. 13 Select one: True…

A: Given the statement

Q: Show (in terms of e - 6) that a function f : [2,7] R be defined by f(z) = V² +1 is uniformly…

A: In this question, we need to show the given function f(x) is uniformly continuous.…

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

A:

Q: If Σ α An diverges then E ca can diverges only if c > 0 only if c < 0 only if c+ 0 for any real…

A: Given, ∑an diverges then find for which values of c, ∑can diverges.

Q: Use the Second Fundamental Theorem of Calculus to find F′(x).

A:

Q: If Σ An diverges then > can diverges O only if c>0 O only if c< 0 O only if c+0 O for any real value…

A: Given, the series ∑an diverges, then we have to find the values of c for which the series ∑can…

Q: Let g=yf(xy). Show that: - მყ У ӘУ дд - X- = g дх

A:

Q: Given that F(x) = a) F'(x) bl 5'(4) 2 1 1 + 2 dt.Using the 2nd Fundamental Theorem of Calculus, find

A:

Q: Use the Second Fundamental Theorem of Calculus to find F'(x). F(x) -TVea+3 dt F '(x) =

A:

Q: Prove, if f(x)= V1+x² –In +1+ 1 is increasing and concave on x X E (0;+∞) .

A: f is increasing if first derivative is positive in the interval  and f has concave if second…

Q: Let F(x)= ^4sqrt(x) A. Find the linearization of F(x) at x=16 B. Use your answer in part (a) to…

A:

Q: Let f (x) belong to Zp[x]. Prove that if f (b) = 0, then f (bp) = 0.

A:

Q: ) For what value of a is fx² -1 x<3 S(x)= { |2ax x23 Continuous at every x?

A:

Q: (b) Use Taylor's Theorem to give the Error Term E, (x) = f (x) – T, (x), as a function of x and some…

A: T2(x)=2+14(x−4)−164(x−4)2 The error term is…

Q: Find the dérivative of the function: f(x)=In(e^x-13x)

A:

Q: Let ƒ(x) = px2 + qx + r be a quadratic function defined on a closed interval [a, b] . Show that…

A: Given,

Q: Man of X = Avenge f= ELK) H.w prove that E (x-x) =0 Hint 又=E(x)

A: to prove EX-X=0 using the property of Expectation  EX+Y=EX+EY therefore, EX-X=EX-EX now let Xi be a…

Q: Given the function F(x) = x3 + x + 2 Defined in an interval of [2, 5], there exists some number "C"…

A: We will find out the required value of C.

Q: If f"(c) = 0, then f(x) cannot have a local extremum at x = c.

A: We know, if f"(c) is negative then f(x) have local maximum at x=c and if f"(c) is positive then f(x)…

Q: Verify that the hypotheses of the Mean-Value Theorem (MVT)are satisfied for the function f(x)=e¬*on…

A: Here, the given function is: f(x)=e-x on [0,2]

Q: 1 dt, for x > 4. In(t) Let F(x) 4

A:

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the g'(x) if: g(x) = 1 +t² dt 3x2

A:

Q: Use the Second Fundamental Theorem of Calculus to find F′(x).

A: It is given that,Fx=∫-2xt2-2tdt We have to use the Second Fundamental Theorem of Calculus to find…

Q: 15. If f+g is differentiable at a, are f and g necessarily differentiable at a ? If f g and f are…

A: Let f be any function that is not differentiable  at the point a and define as: gx=-fx for all real…

Q: Determine if f(x)=In (x² + 1) is uniformly continous on the interval I (-0, +0)

A:

Q: exists depends on as long as tť? <

A:

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

A:

Q: Find f(x) if f(3) = 0 and the tangent line at (x, f(x)) has slope x2 + 5 In (14) f(x) =| 히n 글미(구+ 5)…

A:

Q: 5. Find the linearization L(x) of f at a = 0 f(x) = = 1 = 0 2+x

A:

Q: The domain of the finction f(x, y) = In(-x² - +1) is:

A: The domain of a function is the range of the values that can be input into the function. The…

Q: If f(x) > g(x) >0 for X in [1,0) and g(x) dx diverges to +0, then | F(x)dx also diverges to +. True…

A: It is TRUE, that 0&lt;g(x)≤f(x) for x in [1,∞)  and                               ∫1∞g(x)dx diverges…

Q: (2) Is the function f(x) : R → R, sin a 1 ifa # πh,k & Z, ifa = Tk, k ε Z f (x) Borel measurable?

A: Consider the given function, fx=1sinxifx≠πk,k∈Z1ifx=πk,k∈Z   Thus, the given function have infinite…

Q: Let f(x) = x² In x, where x > 0. Show that f(x) has only one critical point.

A: Given data: The given function is f(x)=x2lnx. The critical point is the point where the slope of the…

Q: _1. There is no function f(x) such that S f(x) = f (x) + C.

A: To determine whether the given statement is True or False.There is no function fx such that ∫fx…