2 3 3 3 - ² Σ [³ ( 5 + + ²) ² - 0 (₁ + + ²)]. = - i n n i=1 integral, that is provide a, b and f(x) in the expression Given Rn , express the limit as n → ∞ as a definite [*f(x)dx.

Q: Express the limit as a definite integral: limn→∞ sec² (1) ΣΩ .) π k=0 4n Of sec(πx) dx O T O Sot…

A: To express the following limit as a definite integral.

Q: Determine the limit of f(x) as x approaches 2. * 51 f(x) 4- 5 4 2 -i 0 i 2 3 4 5 1- -2 3 5+ 3 1 DNE…

A:

Q: If f(x) and g(x) are continuous functions and use the table below to evaluate c'(-1). x -2 -1 f(x)…

A: Consider the table

Q: Express the limit as a definite integral on the given interval. xi* (x)² +9 lim n→ co -AX, [1, 3] dx

A: limn→∞∑i=1nxi*xi*2+9∆x,    1,3

Q: Let f(x) = (Vx + b² - b)/x, b > 0. What is the domain of f? (Select all that apply.) O (-∞, ∞)…

A: f(x)=x+b2-bx The given query is to find the domain of f(x) Also, to define the function such that it…

Q: 1. Function f is continuous on (-00,00). Find constant k. f(x) [kx² + 2x x-kx if x ≥ 2 if x < 2

A:

Q: Let f(x) — sin(nx) n³ n=1 Show that f is differentiable on R and that f' is continuous on R.

A: Within its interval of convergence, the derivative of a power series is the sum of derivatives of…

Q: Explain why or why not Determine whether the following statements are true and give an explanation…

A: We have to determine whether the given statements are true or not: a.  ∫fx f'x dx=12fx2+Cb.  ∫fxn…

Q: Let f(x) be a twice differentiable function on (-o, 0) such that f"(x) is continuous on (-0, 00).…

A: Solution is in next step

Q: 9 f:(-0,0) U (0, ∞) → (∞,0) U (0, ∞0). Where f(x) х Show that f(x) is continuous at x=3 with the…

A:

Q: If that f is continuous on a sxsb. Let F(x) be any of f(x). Then, f(x)dx = F(b) - F(a). This theorem…

A: Recall: Mean value theorem: If f(x) is continuous over an interval [a,b], then there is atleast one…

Q: If fCxl is continuous on [2,7],then Si f(u) dvz f (7)-(2) True e or false?

A: we have given that f(x) is continuous on[2,7].

Q: Find the limit

A:

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

A: