Part 1: Limit of a difference quotient Suppose f(x) : 5 Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box). x - 3 f(7+h) – f(7) lim = lim h0 Part 2: Interpreting the limit of a difference quotient The limit of the difference quotient (your second answer) from Part 1 above is (select all that apply). A. the instantaneous rate of change of f at x = 7. B. the slope of the tangent line to the graph of y = f(x) at x = 7. C. f'(7) D. the slope of the secant line to the graph of y = f(x) at x = 7. E. f(7). F. the average rate of change of f at x = 7.

Q: Question-10 x² +5x + 6 x² - 4 If f(x) = then answer the following: a) lim f(x) x-2 b) State whether…

A:

Q: Show ALL your work and always use correct mathematical notation. 1. The graph of the function f(x)…

A:

Q: V-x – 2 – V3 te lim x--5 -x - 5

A:

Q: x² –1 Evaluate lim X→1 Vx+1 Hint: Direct substitution will result in the expression "O" "O". To…

A: Given: limx→1x2-1x+1

Q: lim x 5x + 6 Example 22. Evaluate 2 X →3 X - 9 |

A: We need to evaluate the given limiting problem

Q: Use the given graph of f to state the value of each quantity, if it exists. If it does not exist,…

A: Since you have asked multiple questions, we will solve the first question for you.If you want any…

Q: x+1 Suppose 8 (x) = Evaluate: lim g(x) x- 2 x-2+ (А) з B + 00 (D) 00

A:

Q: 1) lim (2x² + x + 4) x--1

A: Given limit, limx→-12x2+x+4

Q: x+2 Evaluate lim using table of functional values. X-2 x +8

A:

Q: x² - 6x-8 if x< -1 Evaluate the lim f(x) where f(x) : if x -1

A: Limits of function

Q: Neatly sketch the graph of f(x) and then answer (a) to (d): x² if x 3 YA a) lim,→1- f(x) = b)…

A: fx=x2         if   x&lt;15          if   x=12-x2   if  1&lt;x≤3x-3    if  x&gt;3 The graph is,

Q: z2 - 3 if r 2 3 (a) Calculate lim f(z) and lim f(z). Make it clear which limit is which. +2-

A: x→2+ means x is little more than 2.So, limx→2+f(x)=limx→2+(3x-5)=3(2)-5=1

Q: |x-2| 1 Find the value of lim X →2+ (x-2)

A: Find the limit.

Q: y = f(x) 30 6. -5 -4 -3 -2 -1 3 Figure 1: The graph of y = f(x) 1) Use the graph of the function y =…

A: In the question we have to find the given limits from the graph. NOTE - As per Bartleby's guidelines…

Q: x-2 -1 lim X-3 x+3 Find the limit

A: Given limit is limx→3   x-2 -1x-3we have to evaluate the limit The given limit is of the form of…

Q: Part 1: Limit of a difference quotient Suppose f(2)== Evaluate the limit by using algebra to…

A:

Q: 18 -a+1 Find the limit lim a9 2x2+3x-1

A: Given, limx→918x2-x+12x2+3x-1   To evaluate limit

Q: Let lim, +5 f(x) = -8 and lim, 5 g(x) = 6. g(x) Evaluate lim,5 Evaluate lim, 5 [a2 (9(x) + f(x))]-

A:

Q: An airplane flying at an altitude of 6 miles passes directly over a radar antenna. When the airplane…

A: 1. From figure we can conclude that, Using Pythagorean theorem,  6 ^2 + x^2   = s^2 Differentiate…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.