[3 3. Consider f (x) =- 2х - 3 if x< 0 Find lim f(x) if x20.

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

Q: 1. Use your knowledge of graphs of functions and their derivatives to find the value of lim Show…

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Q: b* – 1 Show numerically that for b = 2 and b = 4, lim x→0 appears to equal In 2 and In 4,…

A: Given limit:

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…

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Q: Given the function f ( x ) = 1 /(x + 3) . Find  lim Δx ⟶ 0 (f ( x + Δx ) − f ( x ))/ Δx

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Q: f(x+h)-f(x) In evaluating lim h-0 in f(x)= x² -1, which is the first step? h

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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…

Q: For all x ≥ 0, 4x − 9 ≤ f(x) ≤ x 2 − 4x + 7. Find limx→4 f(x). ⇒

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Q: Find the value of the limit below. [4 – 6(x + Ax)]? – (4 – 6x)² - lim Ax → 0 Дх Specify the function…

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Q: 2+4r+4 If f(x) = why does f(-2) not exist? Show algebraically that lim f(x) %3D X+2 I-2 does exist.…

A: fx=x2+4x+4x+2 take x=-2 f-2=-22+4-2+4-2+2 f-2=-22+4-2+40 here denominator is zero when x=-2 so the…

Q: b) Find two functions such that lim, 0 f(x) = 0 lim, 0 g(x) = 0 but lim, 0 f(x)g(x) = 1

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Q: f(x) = x²+13z+40 x+5 %3D f(x) f(x) -5.1 -4.9 -5.01 -4.99 -5.001 -4.999 Based on the above, what do…

A: Given ,limx→5x2+13x+40x+5

Q: Determine whether the statement makes sense or does not make sense, and explain your reasoning.

A: Let us consider limx→a-f(x)=A and limx→a+f(x)=B We have, A is not equal to B. When x gets close to…

Q: (fif2..f)is di fferentiable at x, proofthat ... by using f(x)– f(*.) f (x)=lim, x-x,

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

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Q: Find the value of lim f(x) 1 f(x)3= 1+5/x -0.6 -0.5 0.16 01 E -0.6

A: To find out the correct answer.

Q: f(x+h)- f(x) lim where f(x)=4- 2x-x h

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

A: The given function is:

Q: 3. y = f(x) 4 6. -1 lim f(x) =

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Q: b. Determine if the lim f(x) exists, if f(x) is defined as follows: X4 12x + 3, 5x-9, x < 4 x 24…

A: Both question are solved as, follow

Q: Q.4: Prove or disprove, lim f(x) = 4 If f(x) = x # 2 x = 2' I-2

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Q: (4) Consider the function + 3bx + 262 if x 1 For which value(s) of b does lim f(x) exist? Justify…

A: Given: fx=x2+3bx+2b2             if x&lt;1 fx=x-1                             if x≥1 limx→1fx…

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

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Q: Suppose a function f satisfies f(3+h) – 2 lim = 7. Find an equation for the line tangent to the…

A: Let

Q: I if X > 4 and J (X). 4X + 1 i1 X<4. Find lim f(x) x→4+

A: Given; f(x)=√x-1 if x&gt;4 and f(x)=x2-4x+1 if x&lt;4.

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: When the function f(x) satisfies f(1) =1,f'(1)= 3 obtain a value of lim/ (2)" -1 x→1 x² – 1

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

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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.

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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: Use the graph to compute the quantities asked for. y lim, 3 f (x) does not exist -1

A: our objective is to find the limit

Q: 4. What is the sign of a if f(x)= ax' +x +1 satisfies lim f(x) = 0? x→-0

A: Given that fx=ax3+x+1 satisfies limx→-∞fx=∞. Note that the given polynomial having odd degree.

Q: 1 Let F (x) = 1 +2 2< Find lim F (x). 2+

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Q: Fill in the blank/s as shown:

A: we have to fill in the blanks: for the piecewise function defined by f(x)=x2+5      if  x&lt;2x3+1…

Q: x - 2x What is wrong with applying L'Hôpital's Rule to lim x+0 3x – 2

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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: 4x + 1 Let f(x) = x-2 (b) Use the precise definition of the limit (i.e. M, 8) to prove that lim f(x)…

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Q: {x² +7, 14, x = 4 lim f(x), where f(x) =

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Q: x4/7 – 1 lim f'(a) where x→-1 x + 1 f(x) = and a = x4/7 lim x + 1 1 х>-1 II

A: Explanation of the solution is given below...

Q: Q.4: Prove or disprove, lim f(x) = 4 If f (x) = } x # 2 x = 2 x→2 2.

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Q: S -2x? + 5x 7x² – 5 for x 0. According to the alternate form of the definition of the derivative,…

A: Given:

Q: Consider the function - x2, x+1 f(x) = 2, x = 1 O Graph the function f(x). O Find lim,1-f(x) and…

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Q: 2f(x) + 3x – х — 1 15 - Suppose that lim 5. Find lim f(x).|

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

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Q: -10 2468 10 x -4+ ad • +8- -10- Find lim f(x) = %3D

A: The graph of the function f(x) is

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…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: