cos(r + h) + 1 The limit lim h→0 is the derivative of some function f(x) evaluated at x = a. Find the function f(x) and the value of a. h a. f(x) = help (formulas) %D b. a = help (numbers)

Q: Consider the definition of a derivative at a limh→0 f(a+h)-f(x) h We started by thinking about this…

A: 2nd option correct

Q: the limit         limh→0  (√(25+h) - 5)/h represents the derivative of some function f(x) at some…

A: We know that,

Q: f(Xo + h) - f(xo) A continuous curve y = f(x) has a vertical tangent at x = x, if lim = 00 or - 0o.…

A: The solution is given below

Q: f(0 + h) – f(0) Determine whether f is differentiable at x = 0 by considering lim h h→0 f(x) = 18 –…

A: fx=18-x Left-Hand Derivative limh→0f0-h-f0-h=limh→018-h-18-h=1

Q: The limit below represents the derivative of some function f(x) at some number a. 4(3 + h)³- - 108…

A: This question can be solved by applying the concept of first principle.

Q: Let fx) = Vx. %3D Exercise (a) Find f '(a). Step 1 To find the derivative of the function, we will…

A: Let fx=x3. Find f'a To find the derivative of the function, we will use the formula…

Q: Compute the right-hand and left-hand derivatives as limits and check whether the function is…

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Q: 3x 3. Find lim 3х - 1 4. Let I be a neighborhood of xo and suppose that the function f:I→ R has two…

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Q: The given limit represents the derivative of a function at y = f(x) at x = a. Find f(x) and a. 2(3 +…

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Q: f(x) -? The graph of a function f and its tangent line at 0 are shown. What is the value of lim x→0…

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

Q: Question Which of the following is the correct limit definition for the derivative of g(x) = 2"? %3D…

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Q: Let f (x) = Vx + 2 and a = –1. a) Find the derivative of f (a) using the limit definition lim…

A: All the questions are solved below

Q: 1 Eğer lim f(x) = 0 ise, lim f(x)· sin- ? X-C A) -1 B) 1 C) o D) 2 E) mevcut değil

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Q: The limit lim h→0 ((√ 144 + h) – 12)/ h represents the derivative of a function f(x) at a number a.…

A: Given,           limh→0144+h-12h represents the derivative of a function f(x) at a number a.

Q: Find the limit by evaluating the derivative of a suitable function at an appropriate point. Hint:…

A: We first modify the form of the given limit.…

Q: 1. f(r +h)-f(r) Using f'(r) = lim %3D Find the derivative of f(r) = V3x- 4. %3D

A: To find the derivative of f(x)

Q: f(x +h) – f(x) Use f'(x) = lim to find the derivative at x for the given function. h-0 s(x) = 4x + 2…

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Q: Which of the following is/are NOT true I. The limit of a constant is zero. II. Secant line is a…

A: The tangent line of any given function is the line that touches the curve of the function at only…

Q: (a + h) - (a) lim- If =b h , where b is a finite constant, then the function y= a. - f(x) has a…

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Q: f(r+h)-f(x) 1. Use the definition f (x) = lim to find the first derivative for the function h0 h…

A:

Q: f(x+Ax)-f(x) Ay = lim Ax-0 find the derivative of the Using = lim dx Ax-0 Ax Ax following function.…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

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: f(x +h) – f(æ) Use the definition of a derivative f'(x) = lim to show if f' (0)does exist or h→0 h…

A: Given function is : fx=x2sin4x  , x≠00                 , x=0 Squeeze theorem: If xn≤yn≤zn for all…

Q: f(x +h) – f(x) Use f'(x) = lim to find the derivative at x for the given function. h→0 s(x) = 8x + 9…

A: Given  f(x)=2x2-2x+4

Q: f(x+h)-f(x) h Use f'(x) = lim h-0 s(x) = 6x+7 to find the derivative at x for the given function.

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Q: Use the limit definition of the derivative to compute the derivative of the function f(x) = at an…

A:

Q: f(x+h)-f(x) Use f'(x) = lim to find the derivative at x for the given function. %3D h h→0 s(x) 3…

A: 1) Given that s(x)=8x+9 use f'(x)=limh->0 fx+h-fxh find the derivative of s(x) 2) given that…

Q: f '(x) = lim A+-2) if f(x)= ln(x). Use the definition of the derivative to determine if the function…

A:

Q: The limit (8+ h)² – 64 lim h→0 h represents the derivative of some function f(x) at some number a.…

A: We will find the f(x) and a by using limit definition as shown below

Q: The instantaneous rate of change function or derivative of f(x) = |x|: a. is a continuous function…

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Q: f(x+h)-f(x) 1. Let f (x) = Vx find the derivative of the function using the formal definition of the…

A: Given f(x)=xTo find derivative of f(x) usingf'(x)=limh→0f(x+h)-f(x)h

Q: me limit below represents a derivative f'(a) Find f(r) and a lim h-0 (5 + h)² – 25 h. 10

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Q: f(x+h)- f(x) 4x3+9x+5 Using lim0 Find the slope of the tangent line y = Зx-8 h at x = -1.

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Q: 3. Find f'(x) using the definition of the derivative. a) f(x) = 7 lim f'(x) = b) f(x) = 3x %3D

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Q: f(x +h) – f(x) Use f'(x) = lim to find the derivative at x for the given function. h-0 s(x) = 5x + 8…

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Q: Let y = – E. Find the values for A and B so that dy A %3D dx xB where A = -1 V B = 2 V %3D %3D The…

A: using the definition of limit  value of dy/dx is following :

Q: a) Use the limit definition to find the derivative function, h'(x), of the given function h(x). 2…

A: The derivative of f(x) with respect to x is given as limh→0f(x+h)-f(x)h

Q: Given limit represents the derivative y = f (x) at x = a. Find f(x) & a.

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Q: Usc the Definiton, f'cx=lim f (x +h)- fcx), to find ん the derivative for the function fo= -9…

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Q: (d) lim g(f(x)) x6- (e) lim g(x)? x2 (f) lim cos(T f(x))

A: To find the one-sided limits of a composite function say limx→c-g(f(x)), we must first find the…

Q: Use the definition of the derviative to compute the derivative of f(x) = vx + 8 at the specific…

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Q: Activity 1.3.2. Consider the functionf whose formula is f(x) = 3 – 2x. c. Use the limit definition…

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Q: Ise the limit definition of the derivative to compute the derivative of the function f(z) = at an…

A: Given that the function is f(x) =-69+4x Now the definition of derivative is f'(x)…

Q: 2x-2y* If f(x,y)={3x² +3y² if (x, y) # (0,0) then: m if (x,y) =(0,0) f(x,y) is continuous at (0,0)…

A: To check whether the function is continuous or not. Given information: The function is…

Q: f(z)-f(x) Use the formulaf (x) = lim to find the derivative of the following function. %3D f(x) =…

A: Let z = x+h where z tends to x then h tends to 0. Put z in the formula and then put value of the…

Q: te the derivative of f(x) USing the efinition of the derivative lim f(xth)-fx) f(x)=(2-3x)2 %3D

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Q: The limit V4 +h -2 lim h 10 h represents the derivative of some function f(1) at some number a. Find…

A: We know the derivative of f(x) at some number a is defined as f'(a) = limh→0f(a+h) - f(a)h…

Q: The limit,  lim h→0 ((8+h)^2/3 -8^2/3)/h is the derivative of some function f(x) evaluated at x=a.…

A: Given that  At x = a Derivative of the function is  f'(a) = limh→0(8+h)23-823h...... (1)

Q: V16+h–2 This limit lim,→0 represents the derivative of some function f at some number a. State this…

A: The derivative of some function f at some number a is represented by the expression : limh→016+h4-2h

Q: Q.NO.2: i. Find the limit Зх — sin(kx) lim - k + 0 ii. Find the relative extrema using both first…

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