sin 0 - lim 0→ T/6 TT 1/0

Q: Each limit represents a derivative f '(a). Find f(x) and a.

A: Each limit represents a derivative f '(a). Find f(x) and a.                     limh→0sinπ6+h-0.5h

Q: The limit below represents the derivative of some function f(x) at some number a. 10 sin(2 + h) – 10…

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Q: пу Show that if y = ax" where a is a real number and n E N, then dx where x + 0. 1 Given that f(x)…

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Q: The derivative of a function f at a number a is f'(a) = lim if the limit exists. The derivative…

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Q: Let f(x) = Vör. f(x) – f(a) Using the definition of derivative at a point, f'(a) = lim enter the…

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Q: In this example we will show that the function Sa? sin () f(x): if x + 0, if x = 0. is…

A: a) For any point other than x = 0, the values for f(x) and f(x + h) both will be on the continous…

Q: From the definition of the derivative of f(x) as f (x+h)- f(x) f (x)=lim h→0 h derive a formula for…

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Q: Each limit represents the derivative of some function fat some number a. State such an f and a in…

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Q: Let f(x) = 62? – 9. f(x) – f(a) Using the definition of derivative at a point, f'(a) = lim x - a…

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Q: Let f(r) = v5x +2. Using the definition of derivative at a point, %3| a. enter the expression needed…

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Q: Let f(x) = 17 – x? The slope of the tangent line to the graph of f(x) at the point ( – 4, 1) is The…

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Q: (b)Consider the piecewise function S (1+ æ)ª – 1, if x>0 = (x) 6 I sin (4x), if æ < 0. Discover…

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Q: Let f(x) be a function defined in an open interval containing 'a'. The derivatrive of th on f(x) at…

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Q: Using the definition of the derivative, prove that (d/dx)(e^x)= e^x. You will need to use the…

A: To show the derivative of ex is ex, by using the definition of derivative.

Q: The following limit is the derivative of a function f at some number a: V2 +h-V2 f'(a) lim 0-4 h (a)…

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Q: Each limit represents a derivative f '(a).       Find f(x) and  a.

A: limh→ 05+h3-53hSimplify:=limh→ 0h2+15h+75Plug in the value h=0=02+15· 0+75=75

Q: In each of the following, assume that the given equation defines one or more differentiable…

A: Note: Since you have posted multiple questions. We will solve the first question for you. If you…

Q: In each case use the limit definition to compute f'(0), and then find the equation of the tangent…

A: Given: a fx=xex   b fx=x2ex

Q: The following limit is the derivative of a composite function g at some point x = a. sin(x/2 + h) -…

A: We have to find the composite function g(x) at some point x = a using the given limit. Also, find…

Q: Let f(r) = 5I + 2. Using the definition of derivative at a point, a. enter the expression needed to…

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Q: Each limit represents the derivative of some function fat some number a. State such an f and a in…

A: Given: limh→01+h10-1h

Q: 1. þompute and simplify the derivative with respect to x for each of the following functions: a)…

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Q: 2 If x sin x = So f(t) dt, where f is a continuous function, find f(0). (Hint: remember that the…

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Q: Each limit represents a derivative f '(a). Find f (x) and a.

A: Compare the given equation with this:

Q: Each limit represents a derivative f '(a). Find f(x) and a.

A: Given, limh→05h-1h

Q: Which of the following are equivalent to asking "Find the derivative of f (æ) = x² at r = 3 "? %D…

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Q: The limit x°-1 lim x→1 r - 1 represents the derivative of some function f(x) at some number a. Find…

A: We need to find f(x) and value of a.

Q: Find the derivative of the given function using the definition: lim f(x+h)-f(x) h-0 Function: f(x) =…

A: We wil find the value of f'(x) by the required method.

Q: ex+2e-1 X-3 a. lim f(x)= a= b. lim cos(h+1)+1. f(0)= 13 Y y-1/3 y c. lim fy)=

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Q: B. Use the definition of the derivative (the limit of a difference quotient} to find a formula in x…

A: Given function : Using the definition of the derivative formula:

Q: lim h→0

A: F'(x) at x=a is  limh-&gt;af(h)-f(a)h-a

Q: The equation of a tangent line at a point (x₁, f (x₁)) where limh→0 f(x₁+h)-f(x₁) h = +∞ is x = x1.…

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Q: Let f(æ) = /8x. f(x) – f(a) Using the definition of derivative at a point, f'(a) = lim %3D enter the…

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Q: a(sin 2a+cos a sin 2a) lim 1-cos² a a→0

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Q: 3) For each, come up with a function formula that would require the given rules to find the…

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Q: 3. (a) Let f be differentiable on an open interval I and suppose f"(x) = 0 for every x in 1. Show…

A: Let f be a differentiable on an open interval I i.e. (a,b), Suppose that f'(x)=0 for every x in…

Q: The given limit is a derivative, but of what function and at what point? 2-x2 lim r-X r-x

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Q: Find derivative of the following function by using formula f(x)= limit _f(a) - f(x) а -х a→X (3х-1)…

A: To find:

Q: The limit below represents a derivative f' (a). Find f(x) and a. sin ( +h) – 1 lim h-0 h f(x) = a =

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Q: The following limit is the derivative of a function f at some number a: V2 +h - V2 f'(a) = lim (a)…

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Q: Let S(x) = { sin (2) if r#0 if r = 0. if x 0 Is f differentiable at 0? If so, find f'(0). Justify…

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Q: Suppose a and b are real numbers. Consider the function: a) deduct numbers a and b that make f '…

A: Solved below

Q: Let f(x) = The slope of the tangent line to the graph of f(x) at 33 - the point (8, 5) is The…

A: To find the slope and equation of the tangent line of f(x) at the point (8,5).

Q: 24 The following limit gives the derivative of a function f(a) at a point zo: √8th-2 lim h 0 h

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Q: 1. For each function given below, calculate the derivative at a point f'(a) using the limit…

A: we are solving the first questions of three subparts and for the remaining question past the…

Q: The following limit represents the derivative of a function, f, at some number a: cos( + h) lim h>0…

A: Given: The given limit represents the derivative of a function, f at some number a limh→0cos12π2+hh…

Q: exists and is finite, we call this limit the derivative of f at x and say that f is differentiable…

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Q: The graph of f'(x), the derivative of a function f(x), is shown at right. Which of the following…

A: Use the concept of derivative of a function and check all the given options.

Q: Let (a) Show that f(x) is differentiable and that the derivative f(x) is continuous.

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Q: Suppose f(x) is differentiable and one-to-one with f(0) = 1, f(1) = 0, f(2) = -1, f'(-1) = 3, = 4,…

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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: