6. 4 2 4 6 x -6+ 2.

Q: By considering different paths of approach, show that the function f(x, y) has no limit as (x, y) →…

A: Let S be an open set containing , and let f be a function of two variables defined on S, except…

Q: What does it mean for a function to be continuous on an interval?

A: A function is said to be continuous on the interval when the function is defined on every point of…

Q: 2. When can we say that a function is continuous at an interval?

A: We know that when a function does not have any discontinuity, then it is a continuous function. It…

Q: How can we find the Absolute Extrema of a Continuous Function ƒ on a FiniteClosed Interval?

A: How can we find the Absolute Extrema of a Continuous Function ƒ on a Finite Closed Interval?

Q: Find the derivative of the function by the limit process. 9. f(x) = %3D f'(x) =

A:

Q: 5. Use the limit definition of derivative to find f'(x) if f(x) = VT.

A:

Q: what is the largest vertical distance between the graphs of the functions y=x^1/2 and y=x^2 in the…

A: To find the largest vertical distance between the graphs in the interval given

Q: The limit as x goes to zero of x-1 exists.   True or False?

A: We need to say whether the given statement, “The limit as x goes to zero of x-1 exists.” is true or…

Q: Suppose that the tangent line to the graph of a function f at x=2 passes through the point (5,19)…

A: Given that the tangent line to the graph of a function f at x=2 passes through the point (5,19) and…

Q: What can be said about the extreme values of a function that is continuous on a closed interval?

A: To Determine: What can be said about the extreme values of a function that iscontinuous on a closed…

Q: List the x-values where the function is not continuous: f(x) = -x+ 3 if ex if if 3 – x x < - 3…

A:

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

A:

Q: F(X)

A: y = f(x) is continuous at x = a  only if following properties are satisfy : (1)  f(a) exists . (2)…

Q: Please illustrate the difference between a function being continuous and differentiable by…

A: We have to  illustrate the difference between a function being continuous and differentiable…

Q: f(x) = /x +5

A:

Q: Find the largest open intervals where the function is concave upward. 16) f(x) = x3 - 3x2 – 4x + 5…

A:

Q: In terms of limits, what does it mean for ƒ to grow faster than g as x→ ∞?

A: Suppose we need to find out limits  And f(x) grows faster than g(x), Then denominator gets much…

Q: Find the number c which will make the function continuous on (-00, 00). x< 2 f(x) = x+ c, x22

A:

Q: Give an example of a function that is continuous but differentiable at x=2

A:

Q: The limit of the function as x approaches 1 from the left is ... (0/1 Point) 6- 4- 2 -10 -5 5 10 -2-…

A: Given-  To Find- The value of the limit of the function as x approches 1 from the left hand limit.

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: It is defined as the limit of the ratio of the change in a function to the corresponding change in…

A:

Q: how would you, using a limit def. of a derivative at a point find f'(-1) for the function f(x). =…

A: Hint:

Q: Find the absolute extrema of the function on the closed interval.

A: Given,  The function is  y=3-t-3 Interval is [-1,5] The given function is a modulus function which…

Q: 8. If a continuous, differentiable function f is equal to 2 at x = 3 and at x = 5, what can you say…

A: Given that if a continuous, differentiable function f is equal to 2 atx=3 and at x=5, Our Aim is to…

Q: Given the graph below, what can you say about the function at (-1,1)? Not Continuous Continuous

A: The graph of a function is said to be continuous if the value of the function exists for all values…

Q: By considering different paths of approach, show that the function f(x,y) has no limit as (x, y) →…

A:

Q: Find the absolute extreme of the function on the closed interval y = 3cosx ; [0,2π]

A: To find the absolute extreme of the given function.

Q: 12, for f(x) n(x) Estimate the slope of the tangent line at the point x (Use decimal notation. Give…

A: Given,

Q: When can we say that a function is continuous at a number?

A: To explain: The continuity of a function at a point.

Q: Use the limit definition to find the slope of the tangent line to the graph of f at the given point.…

A: Find the slope.

Q: Is the function 1 >-{ f(x) = √x x3 x < 0 0 ≤ x ≤ 1 piecewise continuous or piecewise smooth on [-1,…

A:

Q: Describe the behavior of the function as x approaches 0^+. f(x)=5cotx a. f--> +infinity as x--> 0…

A: Option a is correct answer.

Q: I'm confused on how to put a piecewise function into interval notation

A: To rewrite the definition of the given function using interval notation

Q: 2. Is the function f(x) =² continuous on the closed interval [-1, 1] ? Draw its graph illustrating…

A: Given problem:- Is the function ƒ(x) = 3/x continuous on the closed interval[−1, 1]? Draw its graph…

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x)=√8x+9 at…

A: Here we have to find the instantaneous rate of change of f(x) = √8x+9 at x=1.

Q: 4- х, хS0 10) Determine if the function y(x) =- 3x, is differentiable at x = 0. X>0

A:

Q: Let us try to find where a function is increasing or decreasing given the following. 1. y = 2x –…

A: A function of x is given.We need to find the function is increasing or decreasing in the given…

Q: 3) Use the limit definition of the derivative to find f' (x) if f(x) = - %3D

A:

Q: Sketch the graph of a differentiable function y f(x) through the point (-2,2) if f'(-2)=0 and…

A: Given: To sketch the graph of the differentiable function function y=f(x) through point (-2, 2) if…

Q: What would a graph that is continuous on the intervals (0,2] and (2,3) but not on the interval (0,3)…

A: To discuss the nature of the graph of a function which is discontinuous precisely at the point x=2

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: Sketch the graph of a differentiable function y = ƒ(x) through thepoint (1, 1) if ƒ'(1) = 0 and…

A: Consider the given condition as f'1=0 and f'x&lt;0 for x&lt;1 and f'x&gt;0 for x&gt;1

Q: It is defined as the limit of the ratio of the change in a function to the corresponding change in…

A: Given : what is defined as the limit of the ratio of the change in a function to the corresponding…

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: What does it mean for a function to have an absolute extremevalue at a point c of an interval [a,…

A: When an output value of a function is a maximum or a minimum over the entire domain of the function,…

Q: By the definition show that f(x) = 2 + |x| is a continuous graph at the origin. Also, show the…

A:

Q: 1. Y = 2 – 7.x fa) — 4 — 5х — 21? 2. 3. Y = 2x³ – 3.x

A: