17. Use the limit process to fnd the anea of the negion bounded by the graph of f(x)=2x43 ón the interval [0,3] and x-axis.

Q: 2) Evaluate the limit at x=1 for: x* + 7x2 – x – 2 f(x) x² – 5x + 4

A:

Q: Show that the limit does not exist. (x + y)² lim (7,y)→(0,0) x² + y²

A: We have to check

Q: Q2) Evaluate the limit at x = -2 for: x 1 2x2 4x - 8 S(x) x² - x- 6

A:

Q: 4. Use limits to determine the values of a and b that guarantee the function below is continuous.…

A:

Q: . Let f(x) = x'6/3 – 19x337. Determine the largest n for which f € C" (n-times continuously…

A:

Q: Evaluate the one sided limits of K at x=L algebraically using ly Usina a plecewise formula for…

A:

Q: Express the limit as a definite in 7 lim 1 + (i/n)3 n→ 0 n i = 1 1 7n dx 8

A:

Q: Express the limit as a definite integral. n 7 lim 8 1 + i = 1 n- o n dx

A:

Q: Let            fn(x) = nx/1 + nx2  (a) Find the pointwise limit of (fn) for all x ∈ (0,∞).

A: Given : fn(x)=nx1+nx2; To find the point wise limit of this function for given values of x: We have…

Q: 2. Find the the limit. li -y 1 (tany): 2 Y- 2

A: Given that:                limy→π2-(tan y)π2-y

Q: Show that the absolute-value function y = t(x) = |x − 5| is NOT differentiable at x = 5. (Hint: by…

A:

Q: Express the limit as a definite integral. 7 lim n- 0 n 3 1 + (i/n) i = 1 '1 7n dx 8.

A:

Q: 4. Show that the following limit does not exist by using two paths y = 0 and x =-y lines. x2 lim…

A: We use path y = mx.

Q: f(z) = z2

A: We have to show the given function is not analytic at any point.

Q: find the limit as x approaches infinity of (1+2/x)^x

A: Find the limit as x to infinity,

Q: 4. Evaluate the limit of as e approaches 0. 2a A 2 B. % CO D. infinity

A:

Q: 2. Shows that the function f(x)- x2-9 is continuous at x = 0, but has removable x-3 discontinuity at…

A: This question is taken from the limit in which we have to check the continuity at x=0 of the given…

Q: 9+- Find the limit of f(x)= as x approaches oo and as x approaches 8. x² 8.

A:

Q: 16. Show that f(x) = Vx - 2 is continuous at x=2 but not differentiable at x=2.

A:

Q: 5. Show that x³y³ lim (x,y) →(0,0) 2x¹2 + 3y4 does not exist.

A:

Q: 4. In f(x) = {1– x² if -1sxs 1. Is the function continuous at x=1? Prove. (x² – 1 if x > 1

A: Given Function:                  f(x)={x2-1, if x<-11-x2 if -1≤x≤1x2-1  if x>1    To…

Q: Show that the limit of the function does not exist xy lim (xy)-(0,0) x2 + y?

A: We have to show that limit of the function does not exist.

Q: . Find the maximum value of f(x) = In(x – In x) on the interval -sxs. Show all steps .

A:

Q: Find the value of the.limit Olim Jx+z - V3 X+2 @lim Vx+6 x3-2 X+2

A: A number M is said to be the limit of a function f(x) at x=a if for any arbitrary chosen positive…

Q: 7. Find the limit as x approaches 0. F V I 2 2 O infinity O limit does not exist Oo .

A:

Q: Use two different methods to find the limit where m > 0, n > 0, and x > 0

A: The given limit is: limx→∞lnxmlnxn where, m > 0, n > 0, and x > 0 First method: To evaluate…

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 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: What are the maximum and minimum values of the function y = | x | on the interval -1 ≤ x < 1?…

A: Use the graphical approach to determine the maximum and minimum values of the function y = | x | on…

Q: ind the limit as x approaches two of (2x + x – 10)/(2 – x)

A:

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: 1) Show that the limit doesn't exists : 3x2 Jy 2). lim (x,y)→(0,0) x2 +y²

A: We have considered different paths y = mx. If the limit is independent of m then the limit shall…

Q: Compute the limit 1 e¯nt lim dt. VE n-00

A: Given: limn→∞∫01e-nttdt

Q: Compute the limit as x approaches zero of f(x)=(x^2+3x)/(x^2-x-12)

A: Given : Function f(x)=(x2+3x)(x2-x-12)   To find : Limit of given function when x approaches to…

Q: The limit fx= X2 XスT 2メ-ズ Cos X ,X < TI at Will be 1-itexisted and eanals T 2-It existed and equals…

A: In the question we have to find correct option.

Q: 1. If f:(0, 3) → R is continuous, must its range be an open (possibly infinite) interval?

A: Given statement is : If f:(0, 3) → R is continuous, must its range be an open (possibly infinite)…

Q: Q2: Evaluate: 2 In cosy, [1] limy-o [; y4

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

Q: [1, 2). over Calculate M6 for f(x) = 3 · In(x³) M6

A:

Q: 1) Find the dexivative by the limit process, 2X - 3 3X + 4

A: for a function f(x),f'(x0=limn→0f(x+h)-f(x)hGiven,   f(x)=2x-33x+4  f(x+h)=2(x+h)-33(x+h)+4…

Q: Express the limit as a definite integral. lim 3 Xk, where P is a partition of [2, 3] k=1.k

A:

Q: Find the limit as x approaches -1 for O-1/2 O 1/2 O-1 01 x+2 -1 x+1

A: Concept: L'Hospital's Rule: A general technique for assessing indeterminate forms like 0/0 or ∞/∞ is…

Q: Find the values of m and n that make f(x) continuous over (-∞, ∞): f(x) = m= n= 4 x-2 mx² - nx 2x -…

A: Topic- Limits and continuity

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

A: Yes, existence and value of the limit of a function f(x) as x approaches a depends on what happens…

Q: 29 - For uhat values of a and b is ax+2b x+3a- b くXS2 3X-5 Continuous at every X ?

A:

Q: 1-e X x2 +1 X By using the limit comparison test, the integral

A: Using, limit comparison test

Q: Find the limit of (x3+x2)1/2sin(((2)1/2pi)/x) as x approaches 0

A: To find

Q: draw the graph of a function f on [0, 4] with the given property. Infinite one-sided limits at x = 2…

A:

Q: 5. Conclude on the limit of f(x, y)=y as (x, y) (0,0) along paths y = mx and

A: In this question , we can find the limit along the given path, Firstly we can find limit along the…

Q: Find Tn cebtered at x=0 fir akk b for the function f(x) = 1/(1+x) at a=0

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.