What happens to the function f (x) = 1 + as x approaches to zero.

Q: Let f(x) = x2 – 2.x. Use the definition of the derivative to calculate f'(3) %3D -

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Q: How can I explain what it means for a function f(x) to be O(1)?

A: The 'f(x) to be O(1)' is to be read as function f(x) is of the order of 1.  Now refer to step two to…

Q: At what value of x does the function f(x) =x-2 x change from decreasing to increasing?

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Q: Find the derivative of the function.

A: fx=x3-2x+3x-3

Q: The derivative of f(x) =3 4 is %3D

A: Consider the given function, fx=4x5 The property of derivative is defined as, ddxxn=nxn-1 Convert…

Q: Find the interval/s where the function is increasing and where it is decreasing: f (x) = x³ – 3x + 3…

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Q: Find the first and second derivatives of the functio f(x) = x(x² + 4)2 %3D f'(x) = %3D f" (x) = %3D

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Q: Use the first derivative test to determine the relative extreme values of the function. below. a.…

A: We have to determine the relative extreme values of the function using the first derivative test.

Q: For the function f(x)=2x^3-12x^2+20, Use the SECOND DERIVATIVE TEST to find the relative extrema.

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Q: Find the derivative of the function. f(x) = x2(x − 2)7

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Q: Where is the function f(x) =| x | differentiable?

A: Given information: fx=x The function, after removing modulus function, y=x=x,      x>0=-x,…

Q: Find the derivative of the algebraic function. f(x) = (x2 + 5x + 6)/(x2 − 4)

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Q: The derivative of the function f(x) = 4x-1 is

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Q: Differentiate. f(x) = - 2 e -X t'(x) = ]

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Q: Find the derivative of the function. g (x) = 6x-3 + 2x Og (x) = 18x + 10x-6 %3D Og (x) = -18x-3…

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Q: Find the graph of the function f(x) = [x] + [x/2] from R to R.

A: Given function is fx=x+x2. Definition: Floor function is the greatest integer that is less than or…

Q: Find the derivative of the function f(x) = (3x+2)^2 in two different ways.

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Q: Determine where the function f(x) = √ x / x + 1 is increasing and where it is decreasing.

A: fx=xx+1

Q: Find the points of inflection of the function f(x)=e−x2.

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Q: What rule should be used in getting the derivative of a.)  f(x) = x^5 b.) h(x) = 3(x + 4)^3 c.)…

A: a. fx=x5 The rule used to get the derivative of given function is, ddxxn=nxn-1 The derivative is,…

Q: The best suitable method to approximate a zero of the function f(x) = e* – 1 is:

A: Given f(x) = ex - 1

Q: The best suitable method to approximate a zero of the function f(x) = e* – 1 is: |

A: Given,                 f(x)=ex-1

Q: Find the first and second derivatives of the function. f(x) = √3x-7     f '(x)=   f ''(x)=

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Q: Find the derivative of the algebraic function.

A: The given function is fx=x41-2x+1.

Q: If f(x) = 2x^2 - 10x - 33 , what would the derivative f’(x) be?

A: Given : fx = 2x2-10x-33

Q: Find the derivative of the function. 4 2x - x2 f(x) = %3D x2 - 6 f'(x) =

A: given,        fx=-x2-2x+4x2-6

Q: Let f(x) = }x² – x³. Find the value(s) of x if the second derivative f" (x) equals zero.

A: Use the formula, ddx(xn)=nxn-1 to calculate the derivative. Differentiate f(x) with respect to x to…

Q: Find the values of a and b so that f will be differentiable at x = 3.

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Q: Find the third derivative of the function f(x)=2x^(5)-6x^(4)+7x^2-9x+20

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Q: find the derivative of f(x)= 2x^3 + 4e^3

A: Given information:The given function is

Q: . Give a function f (x) which tends to 0 as x tends to infinity.

A: We have to find a function which tends to 0 as x tends to infinity.

Q: Find the first and second derivatives of f(x). f(x) = 3x – 4x + 2 f'(x) = 2 9x – 4 f''(x)

A: Recall: dxndx =nxn-1.

Q: The function f(x)=(1/(x+1))+4 is decreasing on what interval(s)?

A: Consider the function  fx=1x+1+4

Q: The slope of the line tangent to the graph of f(x) = 18 – 5x² at the point x = -8 O 20 O 10 O 160 O…

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Q: Find the first and second derivatives of the function. f(x) = 11x1 + 6x - x %3D f"(x) = f"(x) =

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Q: Find the derivative of the function. f(x) = (x3 + 7x + 5)(3 +1/x2)

A: To determine: Find the derivative of the function.

Q: Find the derivative of f(x) = -4x 3+4 Provide your answer below: f'(x) = D

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Q: Find the interval on which f(x) =x'e is increasing.

A: We find f'(x) using the product rule

Q: Let f(x) = x-3 Use the definition of derivative to find f'(x). %3D 2C

A: Given : fx = xx-3

Q: Find the first and second derivatives of the function.  f(x) = (x2 + 4)5

A: Rule used:The derivative rules are shown below.

Q: Find the first and second derivative 1. f(x) =x+6x-7x 2. f()=r-7 +2r 3. F(1)=(1+ 7r)

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Q: Find the equation of the line tangent to the graph of f(x)= x2 over (3x-4)3 at the point…

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Q: Find the first and second derivatives of f(x). f(x) = – 3x³ – 7x + 2 f' (x) = f''(x) =

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Q: Rewrite the function g(x) = ((x^2)-1)/((x^2)+2) so that you can solve for the derivative using the…

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Q: find the first and second derivatives of the function f(x) = (x2 + 4)5

A: The given function is f(x)=x2+45.

Q: Find the derivative of the function. f(x) = x3 − 2x + 3x−3

A: Consider the following function: fx=x3-2x+3x-3=x3+x-3 Differentiate fx with respect to x:…

Q: Find the first and second derivatives of the function. f(x) = (x² + 5)5

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Q: Find the first and second derivatives of the function. f(x) = x2/ 1+6x

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Q: Find the derivative of f(x) f(x)= (2x+1)^3(x^2+x)^2

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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.