12. d) If f is continuous on (0, 0) and | f(x)dx converges, then | f(x)dx converges. A can be put into the form x2 - 4 B where A and B are numbers. 12. e) æ(x² + 4) x2 +4

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: Theorem 64. Let {pk}1 converge to point If y # x, then {pk}1 does not converge to y. x.

A: Given that sequence pkk=1∞ converges to point x.

Q: (4) The general solution to 7xy" – y + 10y = 0 is y = A x + x+ x²+ x3 + ... -) +В х x²+ x³ + + x+…

A:

Q: Let f and g be as in the figure, we may deduce that if I g(x)dx converges then

A:

Q: 18 For which numbers a does x,+, = a{x,– x) converge to x* = (a – 1)/a?

A:

Q: 20. Show that if E-1a, converges, then 1 + sin(a,) Σ n=1 converges.

A:

Q: Show that if Σ i=1 converges towards a € R , then lim ) a; = 0 i=N

A:

Q: Consider the sequence of functions {fn}=2 where fn: [a, b] → R defined for n 2 2 by if 0<x s -n² (x…

A: Definition: Suppose fn is a sequence of functions fn:S→ℝ and f:S→ℝ. Then fn→f pointwise on S if…

Q: Suppose {fn}=1 and {g„}=1 converges uniformly on E where {fn}=1 and {gn}n=1 are sequences of bounded…

A: Let fnn=1∞ is converges uniformly to f and gnn=1∞ is converges uniformly to g on E and fnn=1∞ and…

Q: Find the lower bound for the radius of convergence for (x2 + 6x+ 10)y′′+ (x2 −4)y′+ x2y= 0 about x0…

A: Since given point x0 is an ordinary point of the given equation obtain the singular points and thr…

Q: 9. 6) Suppose that g is continuous and that g(x) dx = 2 and g(x) dx = 16. Find g(x) dx.

A:

Q: if 0 ≤ x ≤ 1/ if // ≤ x ≤ 1/1/20 if // ≤ x ≤ 1 n Show that fn converges pointwise to 0, but not…

A:

Q: Let f and g be as in the figure, we may deduce that if | g(x)dx converges then | f(x)dx a a | 4 y =…

A: Given two functions f(x) and g(x) It can be clearly seen that the area bounded by the function g(x)…

Q: The approximation of the root x of the function f(x) = 2x +5-e in the interval [3.4] accurate to…

A: Thanks for the question :)And your upvote will be really appreciable ;) Need 3 iteration

Q: Take any continuous, non-negative function such that lim,oo (a) = +o0, Con- !! struct a setting in…

A:

Q: Find sequences (xn) and (yn) so that xn - Yn 0 and yet does not converge to 1 Yn

A: By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: Suppose that we observe that X1, X2, . . . , Xn  are iid∼ U(0, 1). Show that X(1) converges in…

A: A sequence of random variables Xn is said to converge in probability, denoted as Xn→pX, if…

Q: By using the substitution t² determine the convergence of = S ∞ dx (x+1)√√x*

A:

Q: Show that f„(x) = x" (1– x") converges pointwise V x € (-1,1]. Is f„(x) converges uniformly?

A: When a sequence includes a variable, it becomes a sequence of function. A sequence of function can…

Q: The approximation of the root a of the fanction f(x) -* -Sa +9x +3 in the interval (4,6]accurate to…

A: Substitute 4.5 and 4.6 for x in the function fx=x4-5x3+9x+3 and simplify, to get the values of f(x0)…

Q: Suppose f(x) is continuous and increasing on [a, b], and concave up on (a, b). Is Lo (the Left-Hand…

A:

Q: If f is a continuous function on [0, ∞0) and | f(x)dx converges, then I f(x)dx diverges. 3 Select…

A: Given that, f is a continuous function on [0,∞). And, ∫3∞f(x)dx  converges. Then,…

Q: 4.1 Suppose that fig and g'are continuous on the interval 1= {x :asxs b). Show that a ) exists, and…

A:

Q: If X1, Y1, are two positive unequal numbers and Xn = (xn– 1+ Yn – 1) and y,= Vx – 1 Yn –1 V n 2 2.…

A:

Q: 3. Show that the improper integral x*e*dx is convergent and gives the answer of 4! (It turns out…

A:

Q: 4. Determine whether the function g(x) = roo sin²x converges or diverges by comparing it to f(x)…

A:

Q: If the function f is continuous on [0,00) and | f(x)dx is convergent, then there is a possibility…

A: If the function fIs continuous on [0, ∞) and ∫1∞f(x)dx is covergent, then there  is a possiblility…

Q: 13.D. Show that, if we define fn on R by fa (x) 1+ n?x? then (fn) converges on R.

A: givenfn(x)=nx1+n2x2dividing numerator and denominator by x2fn(x)=nxx21+n2x2x2

Q: 3 B Consider the following function, z= x -2xyty't yn Lind the alues of ag Ddz,z,when redgyel dy 6.

A: Given : z = x2 -2xy + y3 + yw

Q: (b) Prove that the improper integral ]] 8888 converges. dr dy (1 + x² + y2)3/2

A: Solution: Given improper integral, ∫-∞∞∫-∞∞dxdy1+x2+y232 As we know the convergence of the series is…

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: 11. Suppose f and g are continuous positive functions. Provide an example such that diverges and…

A: We need to provide example for convergence.

Q: The sequence a, = sin (A) is unbounded (C) converges to a number less than 1 (E) diverges to…

A: Limit of a sequence

Q: The sequence {(1 + 1)^² +1} 2n O O converges to e² is divergent ez converges to e 2 O converges to e

A: Sequence

Q: 1. For r < 1, define fn(x) = ²x. (a) Prove that for x < 1, k=1 ƒ(x) = lim_ƒn(x) = 84x x(1+x) (1-x)³…

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Q: Suppose that f(x, t) is the probability of getting x suc-cesses during a time interval of length t…

A:

Q: Suppose f(x) > 0 and g(x) > 0 and that | f(x)dx diverges. If f(x) > g(x), what can we conclude about…

A:

Q: 8 Ay 10- f(x) dx using Compute the following estimate of 8- the graph in the figure. 6- S(4) 4- 2-

A: The given graph is  To find ∫08fxdx using Simpson's Rule with n=4

Q: Find the interval of convergence ofS f(x) dx where f (x) = (-1)+(x-6)" %3D E

A: Given problem is :

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

A:

Q: The approximation of the root x' of the function f(x) = x* - 5x +9x + 3 in the interval…

A: Thanks for the question :)And your upvote will be really appreciable ;) Need 3 iteration

Q: Find the derivative of following series: (k + 2) 2k k+1 a) OE (k + 1) (k + 2) 2k k 1 b) OE (k + 2)…

A:

Q: that converges to a function on R ii)show n х 1=0n!

A: For this, we will use the Ratio Test, which can be written for a series ∑n=0∞an as: limn→∞ an+1 an…

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: 2End 2 povel seies expressan for the funchon flx) =dan'(sn) Whal o As interval or convergencl

A:

Q: 7. Let x₁ = a > 0 and Xn+1 = x + 1/x,, for n E N. Determine whether (x,) converges or diverges.

A: Q7 asked and answered.

Q: 7. Suppose (fn) is a sequence of continuous functions on an interval I that converges uniformly on I…

A:

Q: Suppose that f e C(R) and that | If(x)|dx converges. Show then that 2 f(x)| sin nx|dx sx)dx. lim n00

A: