a. Find the Domain for y = = /4 -x + ! 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) = k x = 3 Vx+4-V4 c. Find limx-0

Q: If f(x)=2-3x². O a. O b. O c. lim h→0 lim h→0 lim 30 From first principles select the correct step.…

A: Given :fx=2-3x2

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Q: Find the limit. 2 – 4x². - 9x + 11 lim - 8x + 6x +2 X00 11 OA. 2 ОВ. оо OC. O D. 1 F/N 8

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Q: E valuate Dle followneg: lim メーフ+ 7x" – 4x? + 7x - 2 J +- 3 メ 3x° -8x"+ フメー458 -x一5 x3

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Q: Let f(x) = x² + 3x – 2 f(x) – f(1) a) Find lim x- 1 x+ 1 b) Use your answer in part (a) to find an…

A:

Q: lim V3x² – 6 X-2

A: The given problem is,           limx→23x2-6 Here the function is continuous and defined at x=2, so…

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A: We have to find the limit of this Vector. If the limit 0/0 form, then we can use L' Hospital rule.…

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Q: Verify the limits in a given equation below. (x+h)²-h² lim X→0

A: Verify itx→0lim(x+h)2-h2x

Q: Calculate the following limits. t2 - 2t - 3 lim t43 (t-3)3 a) |x-5| b) lim x+5- x2-4x -5

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

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Q: а) If V5 - 2r s f(x)s V5 – x² for -1sxsl Find lim,o f (x) ?

A: Given that                                5-2x2≤f(x)≤5-x2  for  -1≤x≤1 we have to find…

Q: If the line 3x - 5y = 7 is tangent to the graph of f at the point where x 4 then lim В. A. D. 5 С. З

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Q: Find the limits x² - 7x lim X-o X + 1

A: Given: limx→∞x2-7xx+1

Q: 16. Find the equation of the line tangent to the functionf (x) = 6Vx at x-4. *hint: use lim,a…

A:

Q: Q1) A- Prove that: cotx = - tan-1x B- Find: 1. lịm 2. lim(v9x2 - x- 3x) cotx

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Q: 4. Find the following algebraically. -2x – 4x +4 a. lim x³ – 27 x - 2 b. lim V9x² +1

A: SOLUTION-

Q: Find lim (√2-t, et-¹, In(t + 1)) t-0

A:

Q: Q4)A) Find the following limits (for two only). x+1 1. limx→-1 x2-x-2 1-Vx 2. limx→1 1-x 2х 3.…

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

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Q: 12. Given f(x)=x² – 4x – 5. Find lim fx) –{2) x-2 2

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Q: draw the graph of a function on [0, 5] with the given properties.

A: Removable discontinuity at any point (a) of domain of function (say f(x)) is define as Graphically…

Q: In parts (A)-(C), find the indicated quantity for y = f(x) = 5 – x². A) f(- 1)– f(– 2) (-1)-(-2) f(…

A: Given function is y=f(x)=5-x2f(-1)=5-(-1)2=5-1=4f(-2)=5-(-2)2=5-4=1f(-2+h)=5-(-2+h)2=1+4h-h2…

Q: Use the graphs of f and g and their tangent lines at (-1,0) to find f(x) lim Number x-1 g(x) y f(x)…

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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: In a model of the nervous system, the intensity of excitation of a nerve pathway is given by I = E[1…

A: Given  that: I=E1-e-a(S-h)E

Q: 16. If f(x) = 2x – 1, what is lim x+h h B. - С. —2 D. 2 NIN

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

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Q: B. Calculate the limits of the following functions.. 1. limx¬-1(2X2 + X + 4) 2. limy--2(y3 + 5y – 1)…

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Q: (a) Evaluate the following limit: lim ) (1-e3x x²+3x, x-0 (b) Find the equation of the tangent to…

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Q: 1 Use a plot of f (x) = 4 Vx - 2 to estimate lim f(x) 4 メ→4 | numerically.

A: Given: f(x)=1x−2−4x−4Estimate:limx→4f(x)=?Graphically  and  Numericallly

Q: Show that 16x4+9y12 lim (x,y)→(0,0) 4x²+3y6 does not exist.

A:

Q: 4. Given that f(x)=4x - 3 f (1+h)- ƒ(1) Find lim ,x21

A: Given query is to find the value of indicated operation.

Q: lim (In 2x + 5) + 4 X→ー1

A: Solution:limx→-1ln2x+5+4=ln2-1+5+4

Q: Determine the limit at infinity. 4x -6x2 + 3x lim - -x - 2x+6 O A. 4 OB. OC. 0 D. 4.

A: Given limit is Dividing both numerator and denominator by x^3, we get

Q: Find limx∞ h(x), if it exists, f(x) = 5x3 − 3…

A: Given: fx=5x3-3

Q: Let f(x) = Vx - 1 if x>4 and f(x) = x² – 4x + 1 if x < 4. Find: %3D lim f(x) x→4

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Q: Find the limit. 4) lim (e5/x - 6x)\/2 x-0+

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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…

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Q: Given: f(x) = 4 –x’ and g(x) = Vx+1 a. lim f(x) =

A: Given, fx=4-x2gx=x+1

Q: For f(x) = 2x³ - 2, find ƒ '(x) using the definition f '(x) = lim f(x+h)-f(x) h h→0 f'(x) = Using…

A: Let's find.

Q: Consider g(x)=−7x3+7x2+9. a) limx→0−g(x)= b)limx→−1−g(x)= c)On what interval(s) is g(x)…

A: It can be solved using the limiting definition of continuity

Q: The value of the constant k such that x2-kx+7 lim exits is x-1 x+1 -7 7 -8 8 -6

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Q: The value of the constant k such that x²– kx+6 lim exits is X→1 х—1 б -6 -7 7 -8 8.

A: 1). From the given problem:   fx=2x+14   From the power law:   dxndx=nxn-1.   So,…

Q: Given the piecewise function |x² + 1, if x > c f(x) = | 2æ, 2x, if x <c lim f(x) exists find the…

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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.