Use the limit definition to find the slope of the tangent line to the graph of f at the given point. f(x) = 12 − x2,    (3, 3)

Q: Find the limit and discuss the continuity of the function.

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Q: If f(x) = 4x? + 5x + 3, find f' (-5), using the definition of derivative. f' (-5) is the limit as a…

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Q: Determine whether the limit exists. If so, find its value. If the limit does not exist, indicate…

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Q: Assign values of x using the three special functions, and to get the values of y using scientific…

A: 1. f(t)=sintt   t f(t) 1 0.84147 0.5 0.95885 0.1 0.99833 0.01 0.99998 0.001 0.99999…

Q: Find the slope of the curve y=x2-5x-4 at the point P(3,-10) by finding the limit of the secant…

A: The given equation is y(x) = x2 – 5x – 4 and the given point is (3,–10).Let the other point of…

Q: Evaluate the limit of 6/x^2 as x approaches 0

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Q: What is the limit as x approaches -2 from the left? 3 1 -1 2 r = 2 -1 -2 +00 -2 - 00

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Q: Find the limit by rewriting the fraction first. ху — у — Зх + 3 lim х - 1 (x,y)>(1,4) x+1 ху — у —…

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Q: 14 Find the slope of the function ƒ(x) = -x - 1, by the definition of a limit. Slope =

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Q: 1.Can you easily apply the addition rule for limits to this function? Why or why not? What is the…

A: As per our guideline we are supposed to answer only one question you can repost other questions in…

Q: Determine whether the limit exists. If so, find its value. If the limit does not exist, indicate…

A: To evaluate the given limit substitute x=3 and y=2 in the given function.

Q: Find limit lim (x,y) -> (2,0)   ((Sqrt(2x-y)-2))/(2x-y-4)

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Q: Find the limit by rewriting the fraction first. У + 64 lim (x.y) (8, - 64) x3y- xy + 64x2 – 64x…

A: Consider,limx,y→8, -64y≠-64, x≠x2y+64x2y-xy+64x2-64xTo find: The limit of the given fraction.

Q: Find the limit by rewriting the fraction first. ху - 2у - 2x+4 lim x-2 (x.y)-(2,4) X+2 ху - 2у - 2x…

A: Individually we will find limit for x and y. For limit with respect to x, y=0 and limit with respect…

Q: Find the Limit (when r goes to 0) of the value of the x-intercept of the line PQ and the x-axis.

A: The equation of the pink circle with centre at origin and radius, r is x2+y2=r2. The equation of the…

Q: otf{(16-x*)dx . b. Use the limit definition to find the exact value of

A: Using limit definition calculate given integral

Q: Find the limit, if it exists. Remember to use proper limit notation. Зx2+4х-1 lim х-2 х2-2х 16+x-4…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Find the limits by rewriting the fractions first.

A: Given that limx,y→2,2x+y≠4x+y-4x+y-2.

Q: Differentiate f(x)=√1−x2 by evaluating the limit of the difference quotient. Show all steps, using…

A: Using the limit of the difference quotient we get: limh→0f(x+h)-f(x)h=limh→01-(x+h)2-1-x2h

Q: Explain, using limit definition, why f′(x) = 0 for any constant function f(x) = c.

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Q: Find the limit of the function 2x-1 ists): lim 2r-x x0.5

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Q: Find the limit of the function if it exists lim (x,y)+(0,0) x² + y² - 2xy y³ – x3

A: Given,         lim(x, y)→(0, 0)x2+y2-2xyy3-x3

Q: Determine whether the limit exists. If so, find its value. If the limit does not exist, indicate…

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Q: Use the graph of function f to find the indicated limit f(-2) or function value, or state that the…

A: We have to find the limit

Q: limit as x approaches infinity, 10x^5+x^4+31/x^6

A: Here an expression is x is given to us and we need to calculate the value of expression when x tends…

Q: Find the limits by rewriting the fractions first.

A: Let the given limit be, L=limx,y→1,-1x3+y3x+y Consider the algebraic identity,…

Q: Find the limit by rewriting the fraction first. ху - Зу - 4х + 12 lim x- 3 (х,у) — (3,7) X#3 ху - Зу…

A: we have to find the limit of the given expression

Q: Determine whether the limit exists. If so, find its value. If the limit does not exist, indicate…

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Q: x2 – 3x 4 - - Evaluate the limit: lim x → - 1 5х + 5

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Q: 6) Use the graph of f to find the indicated limit and function value: y 3- 1-3-2-1 -2-

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Q: Divide numerator and denominator by the highest power of x in the denominator to find the limit at…

A: The limit of a function limx→Xfx=Y means that value of  function fx can be as close to Y by making…

Q: Use the limit definition to find the slope of the graph of fat the given point. f(x) -x - 6x; (1,…

A: Given Data: Function: fx=x2-6x ......1 Point: Px, y=P1, -5 Using the limit definition, The…

Q: Find the value of the limit limit x tends to -3 (5-y)4/3

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Q: Evaluate the limit. (If you need to use -o or co, enter -INFINITY or INFINITY.) lim (r-c# -z 12 I…

A: To evaluate the limit limx→-∞x.e12x-x

Q: Guess the value of the limit limx->∞ x2/2xby evaluating the function f(x)  = x2/2x  for x…

A: Evaluate: limx→∞x22x

Q: By considering different paths of approach, show that the function below has no limit as…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: How will you discuss the limit of the function as ? approaches ? and the value of the function as ?…

A: The solution of above question is written below.

Q: Given f(x) = 7- 3x, find f'() using the limit definition of the derivative. f'(x)=

A: NOTE: Refresh your page if you can't see any equations. . substitute x+h for x

Q: Find the limit and discuss the continuity of the function.

A: Given  We need to : i) find the limit. ii) Discuss the continuity of the function.

Q: Given the function y = (x2 – 5x + 6)/(x-2), (x#2), find the left-side limit and the right-side limit…

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Q: What is the limit as x approaches positive and negative infinity?g(x) = (10x^5 + x^4 + 31)/x^6

A: We need to find the limit as x approaches positive and negative infinity for the function given…

Q: Use the limit process to find f'(x) = limh -->0 f(x+h) - f(x)/ h for f(x) = 3/4x-7

A: Use derivative formula :-   f'(x) =  dydx = limh→0f(x+h)-f(x)h

Q: Decide whether the limit exists. If it exists, find its value. 1) lim f(x) x-1 2

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Q: Use limit definition to find f'(2) for the function, f(x) = 3x? – 4x + 1-

A: fx=3x2-4x+1 substitute x+h for x fx+h=3x+h2-4x+h+1 fx+h=3x2+2xh+h2-4x-4h+1 fx+h=3x2+6xh+3h2-4x-4h+1…

Q: Given f(x)= 5x+1,Find lim (x +h)- f(x) h when x>--? h0

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Q: Calculate the limit value: x² – x – 6 lim x--2 x + 2 Select one: O a. 00 b. 0 O C.-5 d. -3

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Q: Find the value of the limit

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Q: he limits of the followi X-2 2. lim х->2 X — 8 x'-8

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Q: By considering different paths of approach, show that the function below has no limit as…

A: In this question we have to find the limit.

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: