1 (a) Use the Integral Test to show that > converges. 2. n' +1 d 1 n = 0 -1 tan dx Hint: 1+x?

Q: The function values f(x) in the table below is increasing for 0Sx< 12. 0 369 12 f(x) 34 35 37 4244…

A: (A)∆x=3Then right hand sum =∆x(f(3)+f(6)+f(9)+f(12))                                =3(35+37+42+44)…

Q: Show that d (x + 1)? 1 (을 tan 'x + t In dx (1 + x)(1 + x²) x? + 1

A: The given function is

Q: 9. TM Integral in this exercise converges Evalvate the Integral without Using a table. 2. -2

A: The limit of an improper integral can be written as: The improper integral converges if the limit…

Q: -1 -1 Differentiate xe 1 2 and hence integrate 2 dx.

A: Let g(x) =x e-12 x2 then x -derivative of g is given by dgdx=ddxx e-12 x2  now , using product rule…

Q: Suppose fn(x) = nx(1-x)" for x = [0, 1]. Show that (fn) converges pointwise but not uniformly to the…

A: Let For For  and so that Then, Thus, Hence, the  sequence  of functions converges  pointwie  to the…

Q: Use integration by parts to prove the reductionformula.

A: Consider the following integration by parts formula: ∫uvdx=u∫vdx-∫dudx∫vdxdx ILATE Rule: We have two…

Q: Suppose the function f(x) is differentiable on (0, ∞) with a continuous derivative and satisfies >…

A: Step 1: Step 2: Step 3:

Q: - 2) Let F(x) = t¹/² = t³/² dt for x > 0. Determine the following: a) F(4) 3 b) F'(4) c) Intervals…

A: Let Fx=∫1xt12-13t32 dt  for x&gt;0. To determine the following. (a) F4 (b) F'4 (c) Intervals where…

Q: actuaZ D X=Ytmacking weigh Şk.(i-cx-3)³), ifɔ 147 f(x)= 0, otherwise (4) k=? SFxsdx=1) →1=…

A: Given, the PMF, fx=k1-x-32, 2≤x≤40, otherwise

Q: (b) 3 – cos(x) 2

A: Follow the procedure given below.

Q: Evaluate the integrals that converge, enter 'DNC' if integral Does Not Converge. 7x (x²+4)² [x da

A: