calc

[lime edge]

put that is lest than or equal to 3 in x^3

u can also put 3 in x^3

when u will solve this u will get the idea of 2nd limit

[ionic summit]

is this correct ?

[untold scarab]

do you know what they mean by the idea of the second limit

[ionic summit]

sorry im not that sure

[untold scarab]

first, do you know what 3^- and 3^+ mean?

[ionic summit]

limit as x approaches 3 from the left and right?

[untold scarab]

yesss

now if you look at g(x),

≤ 3 means "less than or equal to 3" but can also mean "to the left of or equal to 3"

[ionic summit]

ohhh

[untold scarab]

> 3 means "greater than 3" but can also mean "to the right of 3"

so if you only take a left-sided limit,

3^-

then you use x^3 + k for your g(x)

,,\lim_{x\to3^-}g(x)=\lim_{x\to3^-}x^3+k

[proper field]

mtt07734

[untold scarab]

and if you take a right-sided limit with 3^+, you use the right side of 3

[ionic summit]

ohh okayy

[untold scarab]

in both limits, you can directly get them by just plugging x=3 in

for this problem, thats all youll need to solve the limits

you solve one-sided limits like with regular limits

and plugging the number in and seeing if the limit just works is the first step

,,\lim_{x\to3^+}g(x)=\lim_{x\to3^+}kx-5=3k-5

[proper field]

mtt07734

[ionic summit]

ohhh

[untold scarab]

so what would this limit be

[ionic summit]

do i just have to plug in 3?

[untold scarab]

yea

because if it was $\lim_{x\to3}x^3+k$ youd do the same and itd work

[proper field]

mtt07734

[ionic summit]

3^3 +k

[untold scarab]

or k + 27

thats correct

now for the next part

for this function to be continuous, it cant make any jumps

now we know the left side of 3 is the value k + 27

and we know the right side of 3 is the value 3k - 5

if these were different values,

there'd be different values on both sides of 3

and the function wouldn't be continuous, right?

[ionic summit]

yes

[untold scarab]

so they have to be the same value

for the function to be continuous

theres one value of k that makes that happen

how can you solve for this value of k?

[ionic summit]

27+k=3k-5
27+k-3k-5
k-3k=-5-27
-2k=-32
k=16?

oh wait

[untold scarab]

k = 16 is correct

good job

[ionic summit]

does that make it continuous?

[untold scarab]

yea

because left limit = right limit = f(3)

(because in this problem f(3) is using the same thing as the left limit)

[ionic summit]

okay thank u so muchh

[untold scarab]

np

.close

[tight violet]

Solved

Post marked as solved by @untold scarab.

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