Let f be defined by f(x)= 4x^3-2m, x is less than or equal to -1 , 7x^2+5m , x is greater than -1. Piece wise function.
a. Find lim-->-1 from the right side(in term of m)
B. Find lim-->-1 from the left side (in term of m).
I don't get what do they mean by in term of m. plz help.
m is a constant, just as 4 is. From the left side, f(x) at the limit is 7+5m.
Wait don't you mean from the right side is 7+5m and left is -4-2m?
My apologies for the confusion in my previous response. Let me clarify the correct solutions for you.
When they say "in terms of m," it means expressing the limit as a function of the constant m.
a. To find the limit as x approaches -1 from the right side (i.e., x → -1+), we need to consider the function f(x) = 7x^2 + 5m for x greater than -1. Since x is approaching -1 from the right, we plug in x = -1 into this expression to find the limit. Therefore, the limit as x approaches -1 from the right side is:
lim (x→-1+) f(x) = lim (x→-1+) (7x^2 + 5m)
= 7(-1)^2 + 5m
= 7 + 5m
So, the limit as x approaches -1 from the right side in terms of m is 7 + 5m.
b. Similarly, to find the limit as x approaches -1 from the left side (i.e., x → -1-), we consider the function f(x) = 4x^3 - 2m for x less than or equal to -1. Plugging in x = -1 into this expression, we get:
lim (x→-1-) f(x) = lim (x→-1-) (4x^3 - 2m)
= 4(-1)^3 - 2m
= -4 - 2m
Therefore, the limit as x approaches -1 from the left side in terms of m is -4 - 2m.
So, the correct answers are:
a. The limit as x approaches -1 from the right side (in terms of m) is 7 + 5m.
b. The limit as x approaches -1 from the left side (in terms of m) is -4 - 2m.
Again, apologies for the confusion caused.