# calculus again

Suppose lim x->0 {g(x)-g(0)} / x = 1.
It follows necesarily that

a. g is not defined at x=0
b. the limit of g(x) as x approaches equals 1
c.g is not continuous at x=0
d.g'(0) = 1

Thanks.

lim x->0 {g(x)-g(0)} / x = 1.

You can use the definition of the derivative:

g'(x) = Lim h--> [g(x+h) - g(x)]/h

Take x = 0:

g'(0) = Lim h--> [g(h) - g(0)]/h

And h is just a "dummy variable" whose name doesn't matter :)

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩

## Similar Questions

1. ### math

Suppose f and g are continuous functions such that g(3) = 4 and lim x → 3 [3f(x) + f(x)g(x)] = 35. Find f(3).

2. ### Calculus Answer Confirming Not Sure Im Right Help?

Evaluate the lim a. lim x--> 64 (cube root x-4/x-64) (∛x-4)/(x-64) -> 0/0 so then let cube root x = u u-4/u^3-64 u-4/u^3-64 = u-4/u-4(u^2+4u+16) the u-4 cancel each other out leaving lim x->64 = 1/u^2+4u+16 1/64^2+4(64)=16 oddly

3. ### Algebra 2

If y=3 is a horizontal asymptote of a rational function, which must be true? lim x→ 3 f(x) = 0 lim x→ 0 f(x) = 3 **my answer lim x→ ∞ f(x) = 3 lim x→ 3 f(x) = ∞

4. ### No one is helping me :/ ??

If y = 3 is a horizontal asymptote of a rational function, which must be true? lim x→ 3 f(x) = 0

1. ### Calculus

Let f be a function defined for all real numbers. Which of the following statements must be true about f? Which might be true? Which must be false? Justify your answers. (a) lim of f(x) as x approaches a = f(a) (b) If the lim of

2. ### Probability

Let Sn be the number of successes in n independent Bernoulli trials, where the probability of success at each trial is 1/3. Provide a numerical value, to a precision of 3 decimal places, for each of the following limits. You may

3. ### 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

4. ### Calculus Limits

Question: If lim(f(x)/x)=-5 as x approaches 0, then lim(x^2(f(-1/x^2))) as x approaches infinity is equal to (a) 5 (b) -5 (c) -infinity (d) 1/5 (e) none of these The answer key says (a) 5. So this is what I know: Since

1. ### Probability

Let Sn be the number of successes in n independent Bernoulli trials, where the probability of success for each trial is 1/2 . Provide a numerical value, to a precision of 3 decimal places, for each of the following limits. 1. lim

2. ### Calulus Completely lost

Find the indicated one-sided limit, if it exists 1.lim f(x) and lim f(x), where x->0^+ x->0^- 2. f(x) = [2x if x is less than 0] [x^2 if x is greater than or equal to 0]

3. ### Calculus

For the function f whose graph is given, state the following (a) lim x → ∞ f(x) (b) lim x → −∞ f(x) (c) lim x → 1 f(x) (d) lim x → 3 f(x) (e) the equations of the asymptotes (Enter your answers as a comma-separated

4. ### Math

True or False If lim x→∞ f(x) = 1and lim x→∞ g(x) = ∞,then lim x→∞ [f(x)]^g(x) = 1.