This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.Tutorial ExerciseFor what value of the constant c is the function f continuous on (−∞, ∞)?f(x) =   cx2 + 5x      if x < 6x3 − cx if x ≥ 6Part 1 of 2Note that f is continuous on (−∞, 6) and (6, ∞). For the function to be continuous on (−∞, ∞), we need to ensure that as x approaches 6, the left and right limits match.First we find the left limit.lim x→6− f(x) = lim x→6− (cx2 + 5x) = Next, we find the right limit.lim x→6+ f(x) = lim x→6+ (x3 − cx) =

Find each x-value at which f is discontinuous and for each x-value, determine whether f is continuous from the right, or from the left, or neither.f(x) =  x + 6      if x < 0 ex      if 0 ≤ x ≤ 1 6 − x      if x > 1x = (smaller value)continuous from the rightcontinuous from the left    neitherx = (larger value)continuous from the rightcontinuous from the left    neither

f (x) ={ 1x−1 if x 6 = 1;0 if x = 1.(a) Does limx→5f (x) exist? If so, what is it? Try and establish thevalidity of your answer formally using an epsilon-delta argument.If it exists, does it equal f (5)? Is this function continuous at thepoint x = 5?(b) Does limx→1f (x) exist? If so, what is it? Try and establish thevalidity of your answer formally using an epsilon-delta argument.If it exists, does it equal f (1)? Is this function continuous at thepoint x = 1?(c) Is this function continuous?2. Consider the functionf (x) ={x2 if x 6 = 0;−50 if x = 0.2

Let f (x) be defined by: f (x) = 2x /（3 + x） , x ≤ −2 k(x − 2), −2 < x < 4 2x − 6, x ≥ 4 Which of the following values of k would make f (x) continuous on R? a) k = 2 (b) k = 1 (c) There is no such value for k. (d) k = −1

Show that the function given below is continuous at x=−6 . \[ f(x)=\left\{\begin{array}{ll} \frac{3 x^{2}+17 x-6}{x+6} & x \neq-6 \\ -19 & x=-6 \end{array}\right. \] The function f(x) is continuous at x=−6 since f(−6)= and x→−6 lim ​ f(x)= implies that x→−6 lim ​ f(x)∣f(−6)

From the graph of f, state each x-value at which f is discontinuous. For each x-value, determine whether f is continuous from the right, or from the left, or neither. (Enter your answers from smallest to largest.)x = (smallest value)continuous from the rightcontinuous from the left    neitherx = continuous from the rightcontinuous from the left    neitherx = continuous from the rightcontinuous from the left    neitherx = (largest value)continuous from the rightcontinuous from the left    neither