Limits

A function is continuous if the limits to left exist and is equal to the function value.

• True
• False

All rational function is continuous anywhere.

• True
• False

In a rational function f(x), the horizontal asymptote is obtained finding limit when x approaches to plus or minus infinity.

• True
• False

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Polynomial and trigonometric functions are continuous anywhere.

• True
• False

The limit when x approaches to negative infinity of f(x)=-5x is

• 0
• Negative infinity
• Positive infinity
• None of these

If limit when x approaches to positive infinity of f(x)=x/(x²+3) is 0, then the graph of f(x)  has horizontal asymptote at y=0.

• True
• False

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

The function square root of -x is continuos in the interval (-infinity,0].

• True
• False

Tags

CCSS.HSF.IF.B.5

CCSS.HSN.CN.A.1

If f(x)=ax² for x>= 1 and f(x)= x +2 for x<1, and f(x) is continuous at x=1, then the value of a is:

• 0
• 1
• 2
• 3

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

If f(x) is continuous at interval [a,b], and f(a) is positive and f(b) is negative, then f(c)=0, where c is include in [a,b].

• True
• False

The rational function f(x)=(x+2)/(x²-4) has a jump discontinuity at x= -2.

• True
• False