# Calculus

Use pinching theorem to evaluate lim x-->1 ((x-1)sin(1/x-1))

I'm confused in the pinch theorem analytically

1. 👍
2. 👎
3. 👁
1. note that if u = 1/(x-1) then what you have is

sin(u)/u

You have probably seen that this limit is 1, so follow the same argument.

Or, try google. A good discussion is at

math.ucsb.edu/~jcs/SqueezeTheorem.pdf

1. 👍
2. 👎
2. Would it be 0?

1. 👍
2. 👎
3. you are correct. 1/(x-1) -> ∞

I tried to pound a round peg into a square hole.

1. 👍
2. 👎

## Similar Questions

1. ### CALC #

Use Green's Theorem to evaluate F · dr. C (Check the orientation of the curve before applying the theorem.) F(x, y) = y cos x − xy sin x, xy + x cos x , C is the triangle from (0, 0) to (0, 12) to (3, 0) to (0, 0)

2. ### Math

Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. (Select all that apply.) f (x) = sin(x), [0, 2π] If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that f

3. ### MATH *PLEASE HELP

Use Green's Theorem to evaluate C F · dr. (Check the orientation of the curve before applying the theorem.) F(x, y) = y2 cos x, x2 + 2y sin x C is the triangle from (0, 0) to (1, 3) to (1, 0) to (0, 0)

4. ### math

Use the rational zero theorem, Descartes rule of signs, and the theorem on bounds as aids in finding all real and imaginary roots to the following equation: 4x^(3)-17x^(2)+16=0

1. ### mathematics , calculus

verify that the function satisfies the hypotheses of the mean value theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle’s Theorem. f(x)=√x-1/3 x,[0,9]

2. ### Calculus

Determine if the Mean Value Theorem for Integrals applies to the function f(x) = √x on the interval [0, 4]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem. a) No, the theorem does not apply b)

3. ### Calculus

Determine if the Mean Value Theorem for Integrals applies to the function f(x)=2-x^2 on the interval [0,√2). If so, find the x-coordinates of the point(s) guaranteed by the theorem a) No, the Mean Value Theorem for Integrals

4. ### math

Use Green's Theorem to evaluate F(x, y) = y cos x − xy sin x, xy + x cos x , C is the triangle from (0, 0) to (0, 4) to (2, 0) to (0, 0) I kind of understand how to do this , but I am having trouble with the trig

1. ### calc bc (condensed

is the limit as x approaches 0 of sin3x over 3x equal to zero? sorry-- basically this is my problem: lim [sin 3x / 4x) x-> 0 ~~~~I multiplied& eventually got to .75* lim (sin 3x / 3x) x-> 0 ~so i figured since (lim (sinx/x) x-> 0

2. ### Calculus

Determine if the Mean Value Theorem for Integrals applies to the function f(x) = x^3 - 9x on the interval [-1, 1]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem. I think one point is zero.

3. ### URGENT!! PLEASE Calc

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers "c" that satisfy the conclusion of Rolle's Theorem. f(x)=sin4pix , [-1/2,1/2] Well according to Rolle's

4. ### College Algebra

Use rational root theorem and the factor theorem to help solve the following equation X4-2x3-13x2+38x-24=0