If 7х- 5,х <1 { h(x) = 3x2 – x , 1 < x< 3 Is h(x) continuous at (x=1)?

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Given: fx=2x−1x2+3x2+1, and gx=x2+872−3x25 To check whether: f'x=4x2x2−1+2xx2+3−2xx2+12x2−1x2+3x2+1,…

Q: Let f(x)=x^2−8x+5 with domain 0<x<4 Calculate (f^−1)′(−2)

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Q: Suppose that 2 < f '(x) < 4 for all values of x. What are the minimum and maximum possible values of…

A: (a) Given that 2≤f'(x)≤4 for all values of x. By mean value theorem, if f(x) is continues in a,b and…

Q: f(x) = |x| · : %3D Then f-l(x) = if x > 0, and f-l (x) = if x < 0.

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Q: If f(x) = 6(a-3/+7), find f'(2). Find f'(5).

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Q: Let x + 5 f(x) f-'( – 2) = Preview

A: We will find f^-1(x) first. Plug f(x)=y Then switch x and y Then solve for y. Put y=f^-1(x)

Q: Let z +1 f(x) x + 10 f'(- 7) =

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Q: Let x +1 f(x) = x + 9

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Q: Suppose that f(x) (-4)= (2) = = x¹ + 4x³ − 1 - x² Evaluate each of the following:

A: Given query is to find indicated derivative.

Q: The function f(x) = x^2 is decrea sin g on (- ∞,0)  True or False

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Q: If f'(x) = x(x- 2)(x+1), then the graph of f has points of inflec- tion when x = A. -2 and 1 B. 2…

A: f''(x)= x(x-2)(x+1)2  To find the points of inflection of function f  A. -2 and 1 B. 2 and -1 C. 2…

Q: 3x2-7x+8 f(x) = Find f'(x) %3D sin (5x2+9x-6)

A: Here we use division rule of differenciation.

Q: s defined by + x). The value o ind off to 1 decimal

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Q: Find numbers a and b so that f'(1) exists for ax² + b 1 x² f(x) = if if x 1.

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Q: Determine whether the functionf is one-to-one by examining the sign of f' (x). (a)ƒ(x) = x³ + 9x2 –…

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Q: Let ƒ(x) = (7x² − 7)¹ (6x² − 3)⁹ - Find f'(x) = do not oxpand an

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Q: Show that the GHASH function calculates (X1 • H™) Ð (X, · H"-1) © O (Xm-1° H²) O (Xm· H) ...

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Q: Evaluate the step function defined by f(x) = [[x]] for the given value of x. s(-3,4) = I

A: The floor function is the function that takes as input  real number x,and gives as output the…

Q: Let f(x) = In[x³(x + 6) 7 (x² + 5)³]. Find f'(x). 1 3 x²(x+6) ² (x² -5)³ f'(x) =

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Q: if f(X)=(1-2X)^5 then find f`(X)

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Q: Consider the function f(x)=1/(e^x) -2 List all the x values for which the function is discontinuous

A: Consider the function f(x)=1/(e^x) -2

Q: Letf(x) =x^x^xforx >0.Findf′(x).

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Q: If f(x) = e, how many zeros does f'(x) have on the closed interval [0,2x]? (A) One (В) Two (C) Three…

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Q: Show that 2x² + 3x - 5 11x7 ƒ (x) = { is continuous and differentiable at x = 11. x 11

A: Concept If f( x ) is continuous at x = a then limx→a-f( x ) =limx→af( x ) = limx→a+f( x )

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.