2. For the function f(x) defined by O if z is an integer 1 if r is not an integer f(1) = (a) Sketch the graph of y = f(x) for r E(-4, 4] (b) Find limf(r) (if it does not exist, explain why it is the case).

Q: Show that (2o + h)" – 2ö = nz- | n-1 lim h→0 h for any zo E C.

A: To show: limh→0z0+hn-z0nh=nz0n-1for any z0∈ℂ

Q: II. Prove that for each of the following lim (x,y)→(0,0) f(x, y) does not exist. ,2,,2 4. f(x,y) x4…

A: limx, y→0, 0x2y2x4+y4

Q: 2(x-1)* - y² Lex-1)* +2y (d) Show lim does not exist.

A: Limit exist

Q: x – 4 8. Prove that lim Vx = 2 using the e-d-definition. Hint: Va – 2 = VT + 2

A: The epsilon-delta definition of limits says that the limit of f(x) at x=c is  value  of limit. if…

Q: Suppose f(– 1) = 0 g( - 1) = 0 f'(– 1) = 5 g'(– 1) = 4 and all functions are continuous. lim…

A:

Q: 5. Consider the limit: lim x² = 16. What is the largest allowable & that will "work" for e = 0.25 in…

A: Given  f(x) = x² To find : Value of delta using definition of limit

Q: Consider the graph of y = x2/3 = Vx² on the interval [0, 0]. FIGURE 2. The curve y = x2/3. 2 - Show…

A:

Q: 6. Find the limit of f(x) = -- 10 as x approaches co and as x approaches - c lim f(x) = X00 (Type a…

A:

Q: 1. Evaluate the limit for the graph lim f (x). x→1" f(x) 51 4- 3 2 1- -3 -2 -1 1 2 3 4 -1 а. 1 c.…

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

Q: For the function f(x) (X^2-3 if -3 ≤x2 C) is f continuous at x=2? D) does lim f(x) exist at x->4^-?…

A:

Q: Evaluate f(-1+h) – f(-1) lim where f(r) = 5z'+1. Enter I for oo, -I for -oo, and DNE if the limit…

A:

Q: Consider the following. - 1 if x + 0 f(x) %3D -3 if x = 0 y -2 2 -2 Use the graph to find the limit…

A:

Q: Suppose the line L crosses the y axis at 7 and L is Tangent to a function f(x) at the point (5,3).…

A:

Q: |2²–16| a) Evaluate lim using table of T-4 functional value. ах — b, X<1 b) If f(x) = { x? 13x<5 is…

A: Explanation of the answer is as follows

Q: 2x+1 if x 2 Determine the one-sided limit lim f(x). x-2- 2

A: The given function is:

Q: 2x + 1 If t(x) find lim,-o t(x) %3D 8x + 1

A:

Q: Let fn(x) n²x²(1 – x) on [0, 1]. Let e > 0. Does lim,0 m ({x € [0, 1]|fn(x) > e}) exist?

A: Given that fn(x)=n2x2(1-x) on the interval 0,1 The objective is to show whether…

Q: -1, x0 c. lim f(x), where f(x) =

A:

Q: 1. Show that for all f e L'(R) lim %3D

A: Put the delta = 1 in integral function

Q: 2. Consider the function: + 3 if x 2 %3D 17 if x = 2. %3D Find lim, 2 f(x).

A: Function given is- f(x)=x2+3       if x&lt;2x3-1      if x&gt;217           if x=2  To find…

Q: 2) If x3 s f(x) sx for x in [-1,1), find lim f(x) if it exists. x-0 A) 0 B) Does not exist C) -1 D)…

A:

Q: Verify numerically that:

A: To verify: limh→0eh-1h=1

Q: 8-3x, for x <1 For parts b) and c), let f(x)= %3D x+x, for x21' b) lim f(x) x→1

A: We have to evaluate  limx→1- f(x) For x &lt;1 , f(x) = 8 - 3x

Q: * + 2, if x 0' (a) Find lim f(x). (b) Give a simple reason why f is discontinuous at 0.

A:

Q: for |x| > 1, 2x2 fx,(x) = 0, %3D otherwise. Let L = lim P(max{X1,..., X,} < n log(v5)). Determine…

A: Let Xn be a sequence of random variables such that,

Q: Consider the following. x² - 2 if x # -1 if x = -1 f(x) = %3D y -2 -1 1 2 Use the graph to find the…

A: The given function is f(x)=x2-2    if x≠-1-3        if x=-1. Graphically: From the graph, it can be…

Q: x' + 2, if x 0 (a) Find lim f(x).

A: Since , the only point of discontinuity can be zero . For rest of the points on ℝ the function is…

Q: Determine lim g(x) for gas in Figure 11.                   x➔0.5

A:

Q: 1 Let f(x) =. 1,0sx<2 .Determine lim f(x) -x² + 4x – 3, x 22 X2+

A:

Q: Let h(x) = (x2 - 2x - 3)/(x2 - 4x + 3). a. Make a table of the values of h at x = 2.9, 2.99, 2.999,…

A: First, we factor numerator and denominator. Then we simplify for x not equal to 3. Then use this…

Q: In evaluating 2dx E, is same as evaluating lim cos-¹(f(x)). Determine the value of f(x) if x=1.13…

A: Integration

Q: Along the path a = e" find %3D lim (7,y) (1,0) y²-6ry 3r-y-3 O 2 O -2 O-3 O does not exist 0 3

A: we have to find the following limit

Q: Suppose the functions ƒ(x) and g(x) are defined for all x and thatlimx→0 ƒ(x) = 1/2 and limx→0 g(x)…

A: Given limx→0fx=12 and limx→0gx=2we have to findfx.cosxx-1

Q: 3. Consider the function f defined below. Inx for 0<xs2 If f(x)={ then lim f(x) is **]x²In 2 for 2…

A: Given:  fx=lnx         for 0&lt;x≤2x2 ln2     for 2&lt;x≤4limx→2 fx=?

Q: 1. Investigate the limiting behaviour of x2 lim (x,y)¬(0,0) x2 +3xy +y2

A: It given function fx,y=x2x2+3xy+y2. When x,y=0,0 in fx,y=x2x2+3xy+y2 will result in 00. Set the…

Q: If lim as t approaches 4 of the function ((g(x)-6)/(t-1))=1. Find lim t approaches 4 of g(t).

A: The given function is ((g(x) - 6) / (t - 1))  As limit t approaches to 4 the value of the function…

Q: 1(a)Find y' given that y In(2x + 1) + e**+5 %3D 5x2-1 b) Evaluate lim x00 2x2+1 c) Find y' if x'+ y…

A:

Q: (6) Draw the graph of a (a) function ƒ satisfying Y S(1) = 2, S is continuous at 1. What is lim,→1…

A: f(1)=2f is continuous at 1

Q: 1. Prove, using the e-6 definition of limit, that: (a) (b) lim lim_2²+1=2 24-1 x³+x²+x+1= 4.

A: Limit

Q: Suppose that functions g(t) and h(t) are defined for all values of t and g(0) = h(0) = 0. Can…

A: Given that functions g(t) and h(t) are defined for all values of t and g (0) = h (0) = 0.

Q: 2. Let x E (0, 1), use e – d to prove V4 +x – 2 lim 1 4

A: 2. Given x∈0,1, limx→04+x-2x=14                       ... (1) Use ε-δ definition to prove above the…

Q: Find the limit of f(x)

A: Given information

Q: 1.1. Find the limit or show that it does not exist. (a) lim (e + 2 cos 3x) (b) lim vx + ax - x2 + Bx…

A: Note:- In given problem, first problem already has two sub-parts. So, according to guidelines, we…

Q: 1 11 lim X- 1 x2 + 9x – 10 Give your answer in exact form. If the limit does not exist, enter DNE.

A:

Q: 1. Show that for all f e L'(R) lim da = 0.

A:

Q: Discuss the continuity of : Q1 x+ for *く0 for osr 2 Q2 1-x lim

A:

Q: Compute the lim as x goes to 0+ (e^x - 1 - x)/ (xe^x - x)

A: we have to compute the limx→0+ex-1-xxex-x

Q: Suppose that lim, →o(f(x) – 9(x)) = 0 and h(x) is a function with domain R. a) Assume that |h(x) –…

A: We will answer the first question as we only answer one question at a time. Please resubmit the…

Q: at x = 1 and f(1) = 4 at x = 2 andf(2) = 3 10. There is a jump discontinuity 9. There is an infinite…

A:

Q: b. For what value of (k) is the function y=f(x) continuous at x-3. x3-3x2-4x+12 x + 3 x-3 f(x) = %3D…

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.