Consider the following function. f(x) = x^2 − 49 / x − 7 Find each value....

Consider the following function. f(x) = x^2 − 49 / x − 7 Find each value. (If an answer does not exist, enter DNE.)

f(−7) = _____

lim x→−7 f(x) = _______

Determine whether the function is continuous or discontinuous at x = −7. Examine the three conditions in the definition of continuity.

Solutions

Expert Solution

milcah answered 1 year ago

Next > < Previous

Related Solutions

Consider the function and the value of a. f(x) = −2 x − 1 , a...

Consider the function and the value of a. f(x) = −2 x − 1 , a = 9. (a) Use mtan = lim h→0 f(a + h) − f(a) h to find the slope of the tangent line mtan = f '(a). mtan = (b)Find the equation of the tangent line to f at x = a. (Let x be the independent variable and y be the dependent variable.)

Find f(x) for the following function. Then find f(6), f(0), and f(-7). f(x)=-2x^2+1x f(x)= f(6)= f(0)=...

Find f(x) for the following function. Then find f(6), f(0), and f(-7). f(x)=-2x^2+1x f(x)= f(6)= f(0)= f(-7)=

Transformation: Given the function f(x) = 4x3 - 2x + 7, find each of the following....

Transformation: Given the function f(x) = 4x3 - 2x + 7, find each of the following. Then discuss how each expression differs from the other. a) f(x) + 2 b) f (x + 2) c) f(x) + f (2) Unit 6 DQ Follow-up #1: Variation Unit 6 DQ Follow-up # 1 question: If y varies directly as , explain why doubling x would not cause y to be doubled as well. Unit 6 DQ Follow-up #2: Variation Unit 6 DQ1...

7. Find the maximum and minimum of the function. f (x, y) = x^ 2 +...

7. Find the maximum and minimum of the function. f (x, y) = x^ 2 + y^ 2 − xy − 3x − 3y on the triangle D ={(x, y)| x ≥ 0, y ≥ 0, x + y ≤ 4}

Consider the function. f(x) = x^2 − 1, x ≥ 1 (a) Find the inverse function...

Consider the function. f(x) = x^2 − 1, x ≥ 1 (a) Find the inverse function of f. f ^−1(x) = (b) Graph f and f ^−1 on the same set of coordinate axes. (c) Describe the relationship between the graphs. The graphs of f and f^−1 are reflections of each other across the line ____answer here___________. (d) State the domain and range of f and f^−1. (Enter your answers using interval notation.) Domain of f Range of f Domain...

Find the domain for each function please explain. f(x)=10x^2 + x f(x)= -2/x^2

Consider the function f(x)=A(1+x/3) for –1 < x < 1. Find the value of A that...

Consider the function f(x)=A(1+x/3) for –1 < x < 1. Find the value of A that makes this function a pdf. Find the probability that X<1/2. Find the cdf of X. Use the cdf to find the probability that X > -1/2.

5. Consider the function f(x) = -x^3 + 2x^2 + 2. (a) Find the domain of...

5. Consider the function f(x) = -x^3 + 2x^2 + 2. (a) Find the domain of the function and all its x and y intercepts. (b) Is the function even or odd or neither? (c) Find the critical points, all local extreme values of f, and the intervals on which f is increasing or decreasing. (d) Find the intervals where f is concave up or concave down and all inflection points. (e) Use the information you have found to sketch...

1. (8pt) Consider the function f(x) = (x + 3)(x + 5)^2 √ (7 − x)...

1. (8pt) Consider the function f(x) = (x + 3)(x + 5)^2 √ (7 − x) whose first and second derivatives are f'(x) = ((x + 5)(139 + 12x − 7x^2))/2 √ (7 − x) , f''(x) = (35x^3 − 225x^2 − 843x + 3481)/ 4(7 − x)^3/2 . Note: 35x 3 − 225x 2 − 843x + 3481 has three roots: x1 ≈ 7.8835, x2 ≈ −4.3531 and x3 ≈ 2.8982. (a) (1pt) What is the domain of f(x)?...

A. In the following parts, consider the function f(x) =1/3x^3+3/2x^2−4x+ 7 (a)Find the intervals on which...

A. In the following parts, consider the function f(x) =1/3x^3+3/2x^2−4x+ 7 (a)Find the intervals on which f is increasing/decreasing and identify any local extrema. (b) Find the intervals on which f is concave up/down and find any inflection points. B. Consider the function f(x) = sin(x) + cos(x). Find the absolute minimum and absolute maximum on the interval [−π,π].

Subjects