4. lim f (x)=4, where c is any real number エー mil lim[ f(x)" a.

Q: Suppose that lim (x,y)→(3,1) f(x,y) = 6. What can you say about the value of f (3,1)? What if f is…

A:

Q: Evaluate the limitlimx→0+x (ln(x))^2

A: To determine the value of the limit.

Q: A tank contains 1640 L of pure water. Solution that contains 0.03 kg of sugar per liter enters the…

A:

Q: Evaluate the limit: lim_ (x - ln x)* x→0+

A: Using L Hospitals rule , Value of given limit is evaluated.

Q: Suppose that f(x, 0) = 3 for all x ≠ 0 and f(0, y) = 5 for all y ≠ 0. What can you conclude about…

A: The limit of the function, f(x,y) at a point (a,b) does not exist if two paths upon which the…

Q: Find the constant a such that Va ax +4-2 lim

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Q: Use definiction to १r० v of Conkegene to lim n+4

A:

Q: Evaluate the limit: lim (x - ln x)* x→0+

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Q: B) Find the limits by using L.Hopital rule : 7x 1. lim x→0 sin 2x

A: Here we will find out the required value.

Q: TX-1 t. Lim ×つ○ 1

A: limx→0 πx-12x2    +πx(e2πx-1)=limx→0 πe2πxx-πx-e2πx+1+2πx2x2 (e2πx-1)   limx→0 πx-12x2…

Q: lim as x-->0  of (x+1-cosx)/x

A: The given limit of the function:

Q: 8. e 1 Build a table to estimate lim x+0 X

A:

Q: How do you evaluate the limit:  limx-->0  (sin(4x))/9x WITHOUT using L'Hospital's Rule?

A: A property:L'Hospital's Rule is not necessary here.The following is an important property used in…

Q: Find lim (2+x)" * using L'Hôpital's rule. 1/x

A: Given the given expression is limx→∞2+x1x.

Q: sin xy lim 0.

A:

Q: express the limit as a derivative.

A: Given expression

Q: Express the limit as a derivative.

A: To express: limit limx→-1x3+1x+1 as a derivative. Concept used: Definition of derivative:…

Q: 1 () X. lim х+ sin X→+∞

A: The objective of the question is evaluate the limit of the given function.

Q: Evaluate the limit: sinx lim x→0 e4x – 1

A:

Q: 12, Show that the following limits do not exist. (а) lim 1 (x > 0), (b) lim (x > 0), x-0x2 x-0 Vx…

A: Given: d) limx→0sin1x2 to prove limit does not exist.

Q: 9. Build a table to estimate lim sin (Hint: Use multiples of T) X-0

A: Given: To Find:   A table to estimate the value for the given function.

Q: Evaluate the limit. lim     In (Sinh x)x →0+

A: we have to evaluate the limit. lim     In (Sinh x)x →0+

Q: 1. To take the derivative of the following function. х т (1) y = m (2) y = x' log 2. To find out the…

A:

Q: 6. Calculate limit: lim tg x X→0 2-V4+3x

A: Here we have to calculate Limit =limx→0 tgx2-4+3x

Q: Find the limits limx→0+x-1/ln x

A:

Q: The limit lim (n+1-vn- (A) equals-x (B) equals 1 (C) equals ( (D) equals +∞ O(E) does not exist

A:

Q: 5. Apply L'Hopital's rule to determine the limits of the function. y = lim e"(x – a² + 9)

A:

Q: By using the precise definition of the limit of a function show that lim (x,y)→(0,0) 3xy2 /(2x2+ y2…

A: If value of a function at some point is in indeterminate form then we use concept of limit to find…

Q: compute lim as x goes to infinity of ln(x)^1/ln(x)

A: Consider the equation

Q: se L'Hopitals's rule to find lim xIn(e* – 1).

A: Given query is to find the limit of the expression.

Q: If lim f"(x) = +0o, then the trapezoid estimation Tn - | f(x) dx %3D x0* can never be within 10¯³ of…

A: Given that limx→0+f''(x)=+∞ And Tn≈∫01f(x)dx Error for trapezoidal method contains double…

Q: 28. Use the limit definition, lim 7 (x+h)- f(x) to determine the derivative of x-1. [Value of 4] h0

A:

Q: Find the value of the limit: lim x→0* sinx+ tan x

A: Given query is to find the value of the indicated limit

Q: Show using sequences of functions that 2 lim e dx = 0.

A:

Q: lim 0-4 In[(1 + h)² + 1] - ln(2) y

A: To evaluate the given limit .

Q: Q3 (A): By using "L' Hopital rales "; Find the limits of: (1) tim-al-ca (2) lim, x(tan"¹x-x)

A:

Q: Given n ≥ 0;  explain that   limx→∞ fn(x)/(e^x) = 0.

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Q: Use numerical evidence to estimate the value of the limit to at least 2 decimal places. - x – 20 lim…

A: Here we have to evaluate the limit of given function

Q: 1. Use a table of values to estimate the value of the limit. ex – 1 lim x-0 tan x

A: Given: fx=ex-1tanx limx→0ex-1tanx   Note: For tanx, x should be in radian.

Q: Estimate the value of the limit lim, 40 COS x if it exists, by filling out this table and then…

A: We have to find the limit of the function and want to find some values to conclude graphically.

Q: Q2: (a) By using " L' Hopital rul (1) limx¬(1/2)-(tan x)cos x

A:

Q: 1ogx -[X] where,nÎ Nand[.]denotes the greatestinteger function. [x] Evaluate:lim- x®Y

A:

Q: sin(2x) 1) lim

A:

Q: If lim f"(x) = +0, then the trapezoid estimation Tn - | f(x)dx x0* can never be within 10-³ of the…

A: Given that limx→0+f''(x)=+∞ And Tn≈∫01f(x)dx Error for trapezoidal method contains double…

Q: limit x to infinty tan(5t)sec(99t)/t

A: Lim           f∞(st) Sec(q q t )tx→∞    Here limit x→∞ But the function is in t ∴

Q: find the limit lim as x approaches 0 from the right of (square root of x) / (ln (1+x))

A: We need to evaluate the given limit.limx→0+xln1+x

Q: (2+h)* Use the definition of the derivative to evaluate lim h+0 h

A:

Q: Find the limits limx→∞(1 + 2x)1/(2 ln x)

A: Given, limx→∞1 + 2x12lnx We know that, limx→ac·fx=c·limx→afx⇒12limx→∞1+2x1lnx Now,…

Q: f(2) is continuos if lim f(z)=f(z)

A: continuity: A function f (z) is continuous at a point z0 if all three of the following are…