It is defined as the limit of the ratio of the change in a function to the corresponding change in its independent variable as the latter change approaches zero

Q: 6.) Use the limit definition of the derivative to find f' (x), given f(x)=x-3 x+5

A: Consider the function

Q: What are the basic properties of limits of functions of two independent variables?

A: What are the basic properties of limits of functions of two independent variables?

Q: Let f(x)=3−2x+7x^2 Use the limit definition of derivative to find f′(x)

A:

Q: Suppose g is a continuous DECREASING function on the interval [-3,1].

A: 2. As y is a continous decreasing function on the interval -3, 1

Q: 1. How to determine whether the function is continuous or not at a certain point?

A: As per our guideline we are supposed to be answer only one question please repost the other question…

Q: Find the slope of the tangent line to the graph of f(x) = x³ + x at x = 3 using the limits…

A: Given- fx=x3+x To find- The slope of the tangent line to the above function at x = 3 using the…

Q: Sketch the graph of the function f(x). f(x) is continuous from the right at x = 3, but not from the…

A:

Q: When is a function continuous over a closed interval?

A: A function is continuous over a closed interval when it is defined at all points in the interval…

Q: Sketch the graph of a function f such that f′ > 0 for all x and the rate of change of the…

A: Given A function f with f’>0 and rate of change is decreasing.

Q: Let f(x) = 2x² + 1. Use the limit definition of the derivative to find f'(x).

A:

Q: Let f (x) = x² – 4. a. Find f'(x) using the formal limit definition of derivative. -

A: The formula of formal limit definition of derivative is  : lim h →0  [{f(x+h) - f(x)} / h ]

Q: Find the length of the curve of the graph of the indicated function. y = In(sen x), between points…

A:

Q: Use the limit definition of the derivative to show that if f(x) = 1– |x| then -1 ;x > 0 f'(x) = 1…

A: Topic: Functions

Q: If the limit of f(x) is 1 as x approaches 1 and the limit of g(x) is infinity as x approaches 1,…

A: we have to find the limit of the following

Q: Let f(x) = 2x2 + x. Determine f'(1) using the definition of the derivative as a limit.

A:

Q: Find the limit of the function as x approaches 2+.* -5 -4 -3 -2 -1 O 1 DNE Option 5

A: What is the limit of function as x approaches to 2+

Q: ) Let f(x) = 3x – 1. Use the limit definition of the derivative to find f'(x). %3D (3 Marks)

A: Answer - definition of derivative f'(x) = lim h tends to 0 ( f(x+h) -f(x) ) /h

Q: Find the limit of the function as x approaches −1.x^2−4x−5x/x+1limx(→−1)f(x)=

A: Given,

Q: What does it mean for a function to be right-continuous at a point?

A: A function f is right continuous at a point c if it is defined on an interval [c, d] lying to the…

Q: Here is the graph of the function h(x)on the interval (-5, 5), and part of a line tangent to h(x) at…

A:

Q: Find the instananeous rate of change for f(x)= √ X at x=1 using the limit definition

A:

Q: .Find the Global Extrema for f(x) = Bx4-BeB-A)x. Use the second derivative to determine if those…

A:

Q: 3) Let f(x) = 3x – 1. Use the limit definition of the derivative to find f'(x).

A:

Q: Which is the largest interval over which the function shown in the table is increasing?

A: The given function is: To find the largest interval on which the given function is increasing,…

Q: The limit represents the derivative of some function f at some number a. State such an f and a. 16 +…

A: This question is about differentiation expressed as limit of a function

Q: What are the Limits of Continuous Functions?

A: Given, What are the limits of continuous functions?

Q: What does it mean for a function to be left-continuous at a point?

A: function to be left-continuous at a point?

Q: ) Use the limit definition of derivative to compute k'(x).

A:

Q: limit of a function f(x) as x approaches c is always equal to f(x). True or false

A:

Q: The limit of f(x) = sqrt x as x approaches 9 is Infinity 3

A:

Q: The tangent line to the graph of a function f at the point x =2 has x-intercept 10/3 and y-intercept…

A: Given query is to find f(2) and f'(2)

Q: One of the following is a set of linearly dependent functions on the interval (minus infinity,…

A:

Q: find a point c satisfying the conclusion of the MVT for the given function and interval.

A: Given ,y = Cos x - Sin x      0,2πf(x) = Cos x - Sin x

Q: Find the limit of the function f(x) = x²esin(1/x) as x approaches to zero.

A: To find limit of function f(x)=x2esin(1/x) as x approaches to 0. (Using Squeeze theorem)

Q: The secant function is defined as: O hypotenuse adjacent O hypotenuse opposite о adjacent opposite о…

A: Given that secant function defined as

Q: Let f(x) = V5x + 2. Find the derivative f'(x) using the limit definition.

A: We have to find derivative

Q: Estimate the one-sided limits for the function below.  f(x)=(11−x)/(x−8)^2

A: Given:

Q: Is the function continuous or discontinuous? If discontinuous, what condition is not satisfied?

A: Given:

Q: Find the limit of the function, f, as x approaches – 3. x2 – x – 12 - - f(x) = x + 3

A:

Q: Determine the average rate of change of the function on the given interval.  f(x)= 3x2-4 on [1,2]

A:

Q: Find the limit f(X) as x approaches -1 from the left.

A: Graph of f(x) is continuous at x=-1 and f(-1)=2 hence limit f(x) approaches to 2 as x approaches to…

Q: If f is even and differentiable function, the x = 0 is a critcal number of f. True or False

A: Known fact: For even differentiable function, 0 is a critical number.

Q: Is the function continuous at the point being approached?

A: The given function is limy→1sec(y*sec2y-tan2y-1)   We have to check whether this function is…

Q: Let f(x) = 2x2 +1. Use the limit definition of the derivative to find f'(x).

A: We can find f'(x) Using following formula

Q: Not every differentiable function is continuous

A: If a function is said to be differentiable at its domain then it must be continuous in its domain.…

Q: Is the function continuous from X = -5 to x = 0? This function is made up of four (4) linear…

A: 1. True, the function is continous from x=-5 to x=0 as there is no break in the       graph between…

Q: Suppose that a function f whose graph contains no breaks or gaps on (a, c) is increasing on (a, b),…

A: Given, Suppose that a function f whose graph contains no breaks or gaps on (a, c) is increasing on…

Q: In calculus was claimed  that increasing (or decreasing ) functions  defined on a single interval is…

A: Consider a one - to - one function in an fixed interval.  For the function f(x), in the interval 0…

Q: The limit represents the derivative of some function f at some number a. State such an f and a. V81…

A:

Q: Select all of the graphs that depict a function which is not differentiable at x=0.

A: Here, we need to select all the graphs that depict a function which is not differentiable at x=0.…