(c) Use part (b) to show |f(2)| zn+1 Ar + B on Yr pn+1 (d) Use part (b) and the Basic Integral Bound to show 1 |cn| = 2ni f(2) dz zn+1 Ar + B sn (e) Now take a limit as r → o to show c, = 0 for n> 2. Why doesn't this work for n = 1? %3D

Q: Find the local maximum of f(x) = -sin2x – x defined on 2'2

A:

Q: solve y(4)-3y'''+2y''=e3x  using undetermined coefficient

A:

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: Let f be the function defined by ƒ (x) = cos( (/T). (a) Approximate the definite integral| f(x) dx…

A: We have to find the definite integral by using midpoint riemann sum and trapezoidal rule

Q: Let z = e**y* , x = tan¬²(st5) and y = əz Evaluate as (2s+t)²* Select one: O a. 2xy³e{x³y?} t5 t –…

A: Given,

Q: t f(x+y)=f(x)+f(y) + 2xy-1 for all real x and y and f(x) be a differentiable function. [f f^ prime…

A:

Q: 3 а) J(x2 + 2х + 3) dx

A:

Q: Express the limit as an integral. S 4 lim (7(x)² - 2(x ) ³)Ax over [0, 4] n→ ∞ i = 1 2 3 7x²-x³ x)…

A: An integral of a function f(x) in the interval [a,b] represents the area between f(x) and…

Q: What is the indefinite integral of f (x) = x² + 12? f (x² +12) dx = 3 + 12x + C 1 3x³ S(x² + 12)dx =…

A:

Q: Given Lm [(+-«= 2 3 3 3 >I 3 + (i – 1)-) sin( 3 + (i – 1) п i=1 express the limit as n → o as a…

A: Given that

Q: Find the inverse f(x) = 2x - 1. a. r'm =+1 c. r'x) =, d. F'x) = 1 С. %D х-2 b. fx) = X+1 2 -1 %3D 2x…

A: given,           1.  fx=2x-12.  fx=3x2-4x+3  ,  gx=3x-1

Q: Suppose that f: R (0, ∞) and that f'(x) = f(x) ‡ 0. Prove that (f-¹)(x) = 1/x for x > 0.

A:

Q: If f(x)=14-x^(2) and g(x)=\sqrt(x+31), compute g(f(3)). Simplify your answer as much as possible.

A:

Q: K=Zp(t) ,then f(x)=x^p-t is irreducible over K[x]

A: GIVEN: K = Zp(t)

Q: 1. Let f(z) = (z+1) (7-3z++2)z and I = P.V. Aiirear . dx. (x²+1)*(x²-3x+2)x If p Res f(z)|z=-i»r =…

A:

Q: Let g(x) = 2 f(u) + 3 where . u= u = with respect to x? ○ 2. f' (u) +3 O (2. f' (u) + 3) (2x + 2)…

A:

Q: oncave up on (-16/1. creasing on (4/11, 4) a local max at x = 4. an inflection point at x

A: Function: f'(x)=-22x+8(x-4)3f''(x)=44x+64(x-4)4f(x) is continuous in its domain (-∞,4)∪(4,∞)

Q: Evaluate the integral dy (tan ¹(y/8)) (64+ y²) dy (tan¹(y/8) (64+ y²) -

A:

Q: Find the continuous lest squares approximation of degree 2 for f(x) = cos(xx) on [0,1]. %3D

A: Let P2(x)=a0+a1x+a2x2 is the continuous least square approximation of degree 2 for the function…

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: 10 If f is a continuous function and F(x)=f(x) for all x € R, then x)dx=? A © FS) - F)] B ©2[F(5) –…

A:

Q: Suppose f(z) is defined on all of C, is differentiable at z = a, and satisfies f(a) = a. Show that…

A:

Q: Provide your answer below: dx lim n→∞ n WI - sin (6(x; ) − zx; )) . Ax over [2, 6]

A: Given sum is, limn→∞∑i=1n-sin6xi*5-πxi*∆x over 2,6. To Write: the above sum in integral form.

Q: Consider the function F whose criterion is = / dt. 1+ t2 F(x) sena When determining dF/dx the result…

A:

Q: eſt 2 du given that * f(z) dx = 12 f(4Tan¹(u)) 1+u² Evaluate

A: Hint :  This problem is application method of substitution in definite integral. If you have not…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.