(9) Determine whether the improper integral converges or diverges. Evaluate the integral if it converges. (a) foo (b) f L. (c) -∞ dx 16+ 25x² x dx 1+x² x²e² dx (d) [ 2² (e) x²e-³ dx dx x(lnx) 2022 dx 9 - x² (h) ( dx /9 - x² dx √9-x x² ln x dx S²:

Q: Let ƒ(x) = (x³ + 4x + 6) ³ f'(x) = 9x¹ + 12x² f'(1) = 2541 X OF

A:

Q: f(x) = ln[x(x + 6) 5 (x²+2)4] f'(x) =

A:

Q: find the limit when x approaches 1 for equation (x/x-1)-(1/lnx)

A: Step 1:Step 2: Step 3: Step 4:

Q: 4x+7 1<x<2 (ii) If f(x)=< [4x² – 1 determine whether the function f(x) is continuous 2<x<4…

A:

Q: Let ƒ(x) = ln(−5x² + 3x + 10) ƒ'(x) =

A: use logarithmic differentiation

Q: Find value a  such that f(x)={x^2+2x-1 if x not equal to 1…

A: given,f(x)=x2+2x-1  if  x≠1a                if x=1left hand limit at x=1limx→1- f(x)=limx→1-…

Q: xp Vx(x + 5) converges O diverges

A: CONVERGES

Q: lim x → 1- INT(x + 4) =

A:

Q: If an initial amount Ao of money is invested at interest rate i compounded n times a year, the value…

A:

Q: Let 4 f(x) = (a + 4x + 4)* f'(x) = f'(5) =

A:

Q: Suppose that f (x) is a continuous function, f(-1) = 6, f(2) = and f(x)dx: = -3 = T. Evaluate the…

A:

Q: Suppose that a continuous function g satisfies: g(x)dr = 30 and g(2x)dx = 3. 0. 2 Find r9(3x²)dx.

A: Suppose that a continuous function g satisfies: ∫03gxdx=30 and ∫06g2xdx=3. The, we have to find the…

Q: What is the local linearization of f(x) = arcsin(1+4x) near x = −1/4   arcsin(1+4x) ≈

A:

Q: If 7х- 5,х <1 { h(x) = 3x2 – x , 1 < x< 3 Is h(x) continuous at (x=1)?

A: Continuity of function at a Point : Suppose a function f:A→B where A,B⊆ℝ .Then f is continuous at…

Q: Does sin () x 7 converge or diverge? Why?

A:

Q: Find (f-')'(@). 3 f(x) = x + x < 0, a = - 4 (f-1)'( – 4) = Preview

A: The given function is f(x)=x+3x and a=-4

Q: Find

A: We will use the property of laplace transformation

Q: The graph of f is shown in the figure. 6. 4 х 14 -4 -6+ 2-

A:

Q: Expand f(x) = (1+x)^1/2 to the linear order of x and estimate the error when 0&lt;x&lt;1/2.

A: Step 1:Step 2: Step 3: Step 4:

Q: What is the total change of f(x), if ƒ'(x) = 2x − 3x², over the interval [0, 3 -18 -12 -6

A: Given query is to find the total change for the given intererval.

Q: 4. ƒ(x) = (x − 3)(x² + 6x-²) -√2: f'(x) 5

A:

Q: Use a comparison test to determine whether I (ln(x) — 1) dx converges or diverges.

A: (i) If f(x)≤g(x),∀x∈[a,∞) and ∫a∞g(x)dx is convergent,  then ∫a∞f(x)dx is convergent. (ii) If…

Q: If f(x) = (15)× then f'(x) = ? %3D O a) In(15)* O b) In(15)(15)*

A: using differentiation formula

Q: Evaluate Hint: Use differentiation to show that n=1 (1 – x)-2 = nx"-! (for |x| < 1)

A: We have to show that 1-x-2=∑n=1∞nxn-1

Q: If 7x-5,x < 1 h(x) 3x2 – x, 1 < x < 3 Is h(x) continuous at (x=1)?

A: Given: hx=7x-5,x&lt;13x2-x,1&lt;x≤3 We know that any given functiony=fx will be continuous at x=a…

Q: Express the limit as a definite integral where P is a partition of the given interval. limp 1+0 €…

A:

Q: Let ∫∞−∞ f(x) dx be convergent and let a and b be real numbers where a ≠ b. Show that

A: Let ∫-∞∞f(x)dx is convergent and a,b∈-∞,∞ To Show: ∫-∞af(x)dx+∫a∞f(x)dx=∫-∞bf(x)dx+∫c∞f(x)dx     If…