Continuity
Determine wether the function is continuous or discontinuous at x = -2. If it is discontinuous, classify the discontinuity.
g(x) = (3x^3+24x^2+36x)/((x+1)(x+2))
g(x) is discontinuous at x = -2, with a removable discontinuity.
find the limit as x approaches 13 for the function
f(x) = ((x-4)^1/2-3)/(x-13)
The limit as x approaches 13 for the function f(x) = 1/6
find the derivative of f(x) = 6x^3
the derivative of f(x) is f'(x) = 18x^2
Find the AROC of
y=−x^2 +x−1; [0,3]
y=−x2 +x−1; [0,3] = -2
Find the limit of g(x) when as f(x) and h(x) approach x=2
f(x) = -1/3 x^3 + x^2 - 7/3
h(x) = cos(3.14/2 *x)
lim f(x) = -1
lim h(x) = -1
So, the squeeze theorem guarentees that the lim of g(x) as x approaches 2 is -1
determine if f(x) = (4-x^2)^1/2 is continuous from [-2,2]
Yes, the function f(x) is continuous
determine whether the function is continuous at x = 3
f(x){ (x^2-9)/(x-9) if x < 3
9 if x =3
x^2 -3 if x >3
yes the limit is a continuous function at x = 3
Find the derivative of
f(x) = (1+ x^1/2)(x^3)
f'(x) = 3x^2 + 3x^1/2*x^2 + (x^2*x^1/2)/2
Find the AROC of
y=2x^2 −2; [−1,2]
y= 2x^2 −2; [−1,2] = 2
find the lim of f(x) as h(x) and g(x) approach -1
h(x) = -1/4 x^2 - 1/2 x
g(x) = 1/3 x^2 + 3/2 x +2/3
The lim of h(x) = 1/4 and the lim of g(x) = 1/3,
so the squeeze theorem does not guarantee that the limit of f(x), but if it does exist, it would be between 1/4 and 1/3
define f(x) continuity at x = 2
f(x) = (x^2+9)/(x^2-4)
no, the function is not continuous at x = 2 with a removable discontinuity
evaluate the limit of f(x) = (x^2)/(lnx) as x approaches 1 from the left
The lim of f(x) is - infinity as it approaches 1 from the left
Find the derivative of
f(x) = (x^3 + 3)^5
f'(x) = 5(x^3 + 3)^4 * 3x^2
Find the IROC of
y = -x^2 + 2; x = 1
y = -x^2 + 2; x = 1, = -2
Use the Squeeze theorem to evaluate the lim of f(x) = xsin(1/x) as x approaches infinity
The Squeeze theorem guarantees that the limit of f(x) as x approaches infinity = 0
determine whether f(x) = (x^2 -x -2)/(x^2 -5x -6) is continuous at x=6
No, the function f(x) is not continuous at x =6 with an infinite discontinuity
Find the limit as x approaches 0 for the function f(x) = (1/(x+6)- 1/6)/x
the limit as x approaches 0 for the function f(x) = -1/36
find the derivative of
f(x) = (-2x^2 + 1)^1/2
f'(x) = -4/(2(2x^2 + 1)^1/2)
Find the AROC of
y=x^2 +x−1; [−2,−1]
y=x^2 +x−1; [−2,−1] = -2
Use the Squeeze theorem to evaluate the lim of f(x) = x^2 sin(1/x) as x approaches 0
The Squeeze theorem guarantees that the limit of f(x) as x approaches 0 = 0
determine whether f(x) = (x(x-2))/(x-3) is continuous at x=4
Yes, f(x) is continuous at x=4
Evaluate the lim of f(x) = (2x^3)/(x^2) as x approaches infinity
The limit of f(x) as x approaches infinity is 0
Find the derivative of
f(x) = (x^1/2)/(x^3 +1)
f'(x) = ((x^3+1)/2x^1/2)-3x^1/2*x^2)/ (x^3+1)^2
Find the AROC of
y=−x^2 −2; [1,2]
y=−x^2 −2; [1,2] = 3
Use the Squeeze theorem to evaluate the lim of f(x) = x^4sin(7/x) as x approaches 0
The Squeeze theorem guarantees that the limit of f(x) as x approaches 0 = 0