Question

Prove that f(x)=x*cos(1/x) is continuous at x=0. please give detailed proof. i guess we can use...

Prove that f(x)=x*cos(1/x) is continuous at x=0.
please give detailed proof. i guess we can use squeeze theorem.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
(i) Use the Intermediate Value Theorem to prove that there is a number c such that...
(i) Use the Intermediate Value Theorem to prove that there is a number c such that 0 < c < 1 and cos (sqrt c) = e^c- 2. (ii) Let f be any continuous function with domain [0; 1] such that 0smaller than and equal to f(x) smaller than and equal to 1 for all x in the domain. Use the Intermediate Value Theorem to explain why there must be a number c in [0; 1] such that f(c) =c
use the squeeze theorum to show that *** please show work limx→0 cos(x)x^8 sin(1/x)=0 limx→0 tan(x)x^4...
use the squeeze theorum to show that *** please show work limx→0 cos(x)x^8 sin(1/x)=0 limx→0 tan(x)x^4 cos(2/x)=0
Let a > 0 and f be continuous on [-a, a]. Suppose that f'(x) exists and...
Let a > 0 and f be continuous on [-a, a]. Suppose that f'(x) exists and f'(x)<= 1 for all x2 ㅌ (-a, a). If f(a) = a and f(-a) =-a. Show that f(0) = 0. Hint: Consider the two cases f(0) < 0 and f(0) > 0. Use mean value theorem to prove that these are impossible cases.
Prove that {n^3} does not converge to any number. please give me detailed proof, thanks
Prove that {n^3} does not converge to any number. please give me detailed proof, thanks
Prove or give a counterexample: If f is continuous on R and differentiable on R∖{0} with...
Prove or give a counterexample: If f is continuous on R and differentiable on R∖{0} with limx→0 f′(x) = L, then f is differentiable on R.
Is the function continuous on (-infinity, infinity)? Explain. f(x) = cos x; if x<0 0; if...
Is the function continuous on (-infinity, infinity)? Explain. f(x) = cos x; if x<0 0; if x= 0 1-x^2 ; if x>0
Use the Mean Value Theorem and the fact that for f(x) = cos(x), f′(x) = −sin(x),...
Use the Mean Value Theorem and the fact that for f(x) = cos(x), f′(x) = −sin(x), to prove that, for x, y ∈ R, | cos x − cos y| ≤ |x − y|.
Prove that if f(x) is a continuous function and f(x) is not zero then g(x) =...
Prove that if f(x) is a continuous function and f(x) is not zero then g(x) = 1/f(x) is a continuous function.   Use the epsilon-delta definition of continuity and please overexplain and check your work before answering.
Prove or give a counter example: If f is continuous on R and differentiable on R...
Prove or give a counter example: If f is continuous on R and differentiable on R ∖ { 0 } with lim x → 0 f ′ ( x ) = L , then f is differentiable on R .
Suppose that X is continuous random variable with PDF f(x) and CDF F(x). (a) Prove that...
Suppose that X is continuous random variable with PDF f(x) and CDF F(x). (a) Prove that if f(x) > 0 only on a single (possibly infinite) interval of the real numbers then F(x) is a strictly increasing function of x over that interval. [Hint: Try proof by contradiction]. (b) Under the conditions described in part (a), find and identify the distribution of Y = F(x).