(2x-1, x<0 f(x)=- a =0 x+4x-1, x20'

Q: sify whether f(x) is continuous or discontinuous at the point/s. If disco x – 2 x <-1 f(x) = { x² +…

A:

Q: х+ 2 if x 0

A: The given function is  f(x) = x+2ifx&lt;02x-2ifx≥0

Q: Find the limits. Are the functions continuous at thepoint being approached? lim x →1 cos-1 (ln √x)

A: We find the limit by substitution

Q: (b) f(x) - (x + 2x')', a- -1

A:

Q: Estimate the limit of the following functions from the left and from the right and then state…

A: We have to find the limit from the left and right.

Q: Let f(x) { Calculate the following limits. Enter "DNE" if the limit do f(x) = 10- x - x² if x ≤ 4 if…

A:

Q: 2. Given the function f(x) = ., determine if the function is continuOus or not. Identify the point/s…

A: Given function f(x)= (x2-1)/(x-1) is continuous or not , determine type of discontinue.

Q: sin(xy) lim (x,y)-(0,0) x²+y² x²+(y-1)²-x³ lim (x,y)¬(0,1) x²+(y-1)²

A:

Q: find the horizontal asymptotes of the function by computing the limits at infinity.

A: Given the function:

Q: Consider the piecewise defined function x² + 2x – 1 if x 0 ° Which of the following statements is…

A: As we know that,  the function fx is continuous at a point  x=a if the left-hand limit is equal to…

Q: find limit that represents the slope of the tangent line to the following function at x = 2 ? 2 f(x)…

A: Given function f(x)=24-3x To Find that represents the slope of the tangent line to the following at…

Q: Express the limit as a definite integral on the giveninterval.

A:

Q: Express the limit as a definite integral. [Hint: Consider f(x) = x*.] lim n- 00 dx

A:

Q: Sketch the graph of the following function and use it to determine the following limits. If a limit…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Sketch the graph of the following function and use it to determine the following limits. If a limit…

A:

Q: Based on the given values, is the function continuous or not? If not, select the condition which is…

A: In the given question we have to tell such function which satisfies the given three property and and…

Q: Use limits to determine if f(x) = is continuous at z = -2. (z+2)²

A: Given that  f(x)= 1(x+2)2 is continuous at x = -2

Q: Find the following limit. Is the function continuous at the point being approached? lim 2. Cscx+23…

A: We have to solve the limit and  check weather it is continuous or not

Q: Use a graph to determine whether the given function is continuous on its domain. H Sx + 2 if x < 0…

A: Given query is to find function is continuous not.

Q: Use the given graphs of the function f (left, in blue) and g (right, in red) to find the following…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others parts…

Q: Calculate if possible the limits at x = a of the following functions

A: Given, To Evaluate

Q: Because of their connection with secant lines, tangents, and instantaneous rates, limits of the form…

A:

Q: Use the graph of the function f to find the limits at the indicated value of a, if the limit exists.…

A: The graph of the given function is as shown below : limx→a-fx=limx→0-fx=2∴ limx→a-f(x) = 2

Q: Determine if the polynomial or rational function is continuous at the given value of c. If the…

A: Given that: 1. f(x)=(3-x)1/5; c=2   NOTE: As per our answering guidelines, we can only answer 1…

Q: If f is defined on [0, +inf] and Lebesgue integreable, uniformly continuous function, then, lim_(x…

A: Given If f is defined on [0, +inf] and Lebesgue integrable, uniformly continuous function, then,…

Q: Sketch the graph of the following function and use it to determine the following limits. If a limit…

A: To sketch the graph of given function and find the limits

Q: For each pair of functions, use the basic functions (when possible) to say which approaches its…

A:

Q: The L'Hospital's rule can be applied to find the limit of a function as long as you can express it…

A: L'Hospital's rule states that, the limit of the ratio of two functions is equal to the limit of the…

Q: 1 (a) What type of discontinuity does the function g(x)=- have at el/x – 1 x=0 ? Explain. (b) For…

A: This question is from limits and continuity.

Q: Find the limit as x approaches infinity of f(x) when f(x) is x times square root of x

A: x times sqrt(x)= x times x^(1/2)= x^[1+1/2] = x^(3/2)

Q: Find the following from the graph of the function f(x) a) lim f(x)+ S(1) = b) Is the limit f(x)…

A: Graph of the function is given, we have to find its limit

Q: Use l’Hôpital’s rule to find the limits

A: We have to find the limit using L' Hospital's rule: limx→0sin x-xx3 We know in L' Hospital's rule we…

Q: From the function H defined by sections a) Estimate the following limits: lim x→1/2h(x), lim…

A:

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: Does the existence and value of the limit of a function ƒ(x) as x approaches c ever depend on what…

A:

Q: This question has several parts that must be completed sequentially. If you skip a part of the…

A:

Q: „100

A:

Q: Use the limit definition of the derivative f (x) – f(a) f'(a) = lim - a to find f'(a) in each case.…

A: Given fx=x3-7

Q: Q3) If the function {2x +1 lx² + 2 x> h) x <hS f(x) = having limit at x = h. Find the value of h.

A:

Q: 9. Sketch the graph of the following functions and the indicated limit if it exists. Determine if it…

A: The given function,f(x)=x+3if x&gt;22x+1if x≤2

Q: 8. Sketch the graph of the following functions and the indicated limit if it exists. Determine if it…

A:

Q: Explain the difference between a function f(x) being continuous at the point x=a and the limit…

A: We need to find the difference between function is continuous at x=a and limit exists at x=a

Q: 1. Find the points at which f is discontinuous. At each of these points, state the type of…

A:

Q: O3: A- Find the limit for the following functions: - tan2x 4х-3 3x3-9x2+x-3 1- lim x→0 sin4x 2- lim…

A:

Q: f(0) = 1, f"(x) < 0 for x # 0, lim f'(x) = +0, lim f'(x) = -00

A:

Q: Consider the following piecewise defined function: Sr+5 | 4Vx +1 if x 2 3 if x < 3 f(x) = (a) Show…

A:

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

A: The slope of the tangent line m to the graph of fat the given point x0,fx0 is expressed as-…

Q: Find the limit for the following functions: x-sinx 1-lim, x-Vx² + 2x 2- lim,-o

A:

Q: f(x) = 1 16 f(x) -0.26 -0.251 -0.2501 -0.2499 -0.249 -0.24 lim X--0.25 f(x) =

A:

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.