# Continuous Functions - Page 2

Questions

- On what points does f(x)=(lnx)^2 continous?
- How do you use the definition of continuity and the properties of limits to show the function is continuous #F(x)= x+sqrt(x-1)# on the interval [1, inf)?
- How do you use the definition of continuity and the properties of limits to show that the function #f(x) = 5x^4 - 9x^3 + x - 7# is continuous at a given number a=7?
- How should f(2) be defined so that f is continuous on (0, ∞) ?
- How do you use the definition of continuity and the properties of limits to show the function is continuous #F(x)= (x^2-8)^8# on the interval (-inf, inf)?
- How do you use the definition of continuity and the properties of limits to show that the function #f(x)=x^2 + sqrt(7-x)# is continuous at a=4?
- Is the graph of #f (x) = (X^2 + x)/x# continuous on the interval [-4, 4]?
- How do you use the epsilon-delta definition of continuity to prove #f(x) = x^2# is continuous?
- How do you use the definition of continuity and the properties of limits to show that the function #h(t)=(2t-3t^2)/(1+t^3)# is continuous at the given number a=1?
- How do you use the (analysis) definition of continuity to prove the following function #f(x) = 3x +5# is continuous for all x in R?
- Limit as x approaches infinity (x+2)/(x+3)?
- Determine the values of a and b that make f(x) continuous. a=? b=?
- At what point is #f(x) = x - [x]# discontinuous?
- Given #f(x) = ln(1+x^2 tan x)/sin x^3# when #x!=0#, what value do we need to assign to #f(0)# in order to make #f(x)# continuous at #x=0# ?
- The function f (x) is defined as #f (x) = {(-1, x ≤ 0),( (x + 2) ^ 2, 0 < x ≤ 3),(x, x > 3):}#. The area under the f (x) curve between x = (-2) and x = 5 is? Options: a) 27 b) 205/3 c) 155/3 d) 80
- What is #\lim _ { x \rightarrow 0} \frac { - 2} { x ^ { 2} + 1}#?
- For what value(s) of k is the function f(x) continuous at x = -3 given #f(x) = -6x - 12# when x < -3, #f(x) = k^2 - 5k# when x = -3 and f(x) = 6 when x > -3?
- Why is the domain of the function #ln((2x)/(2+x))# x<-2, x>0?
- What is the limite x approaches 0 ((x/(x+1))^x?
- How do you find the intervals on which the function is continuous given # y = sqrt(5x + 9)#?