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Q: Determine the smallest value of the constant a for which the graph of the function f(x) = a^x−x is…

A: Since f(x) should always be greater than x axis ⇒f(x)>0ax-x>0ax>xTake log both…

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?

A:

Q: Express the function in the form   f ° g  ° h

A: We will use the most inner function=h(x), then next one=g(x), and the outer one=f(x)

Q: Find two nontrivial functions f(x) and g(x) so f(g(x))=(−4+4x)^4 outside function f(x) = ? inside…

A:

Q: Find the domain of function defined as follows. y = ln(x2 - 16)

A: y=lnx2-16Domain:       The domain of a function is the set of all possibleinputs for the function

Q: The domain of the function y= f(x) is (Type your answer in interval notation.)

A:

Q: Consider the functions :  f(x)=√x and g(x)=x-1 Solve for- (f°g) (x)

A: Given:

Q: How are the functions f and g given by f (x) = (1.05)ª and g (x) = eº.05z similar? How are they…

A:

Q: Describe the domain of the function f(x, y) = ln(7−x−y).

A: (18)

Q: (c) F{-h(x+ 1) + 2h(x) – h(x – 1)}, where h(x) is the unit step function defined on page 235 of the…

A:

Q: At what value of x does the function f(x) = 3 x- x change from decreasing to increasing? %3D

A:

Q: Find the domain of the function. f(x) = ln(x^2 + 1)

A: Definition used:The domain of a function is the complete set of possible values of the independent…

Q: Locate the discontinuities of the function. 2 f(x) = 1 + e7/x

A:

Q: Differentiate f (x)  = e(1+x)3

A: Given: f(x) = e(1+x)3 To find: The derivative of the given function.

Q: Find the domain and range of the function f(x, y) = ln(5 − x − y)

A:

Q: Differentiate the given function: g(x) = sec¯ ec- (x²) ...

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Q: For what x-value(s) is this function not differentiable? x² – 9 f(x) x + 3

A:

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: 3) Let f (x) = e=x² Where is y'> 0? What does this tell you about the original function?

A:

Q: Find an equation for f(x) using the secant function. (x) f(x) 10 x 3 -2 n 2) 2. 4. 6.

A: we will find the equation of fx using secant function. Let a function: fx=asecx By using graph we…

Q: Find the domain of the function. f(x) = √(ln x)

A: To find domain of the function fx=lnx. Solution: Domain is the input value for which a function is…

Q: Determine the absolute extrema of the function f(x) = (x-3)e* on the interval -2 ≤x≤1.

A:

Q: 10) What is the domain of the function f(x) = Eo?

A: Domain

Q: Find the domain of the function g(x) = /1 – x ln x

A: We have to find domain

Q: Differentiate the function. f(x) = e2 f'(x)

A:

Q: Find the inflection points of the function f(x) = ln(x^2 + 1)

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Q: 14. Use the curve sketching procedure to analyze the function. a. y-x'+x²-20x а. 1+x? b. y=- 1-x?

A:

Q: Where is the function y =4x/x-3 concave downward? Show mathematical work to clearly answer this…

A: For a given function y=f(x) the curve is concave downward in an interval I when the second…

Q: Find the domain of the function: h(x) = ln x2

A: h(x)=ln x2

Q: Apply the definition to differentiate the following functions: 1- y = ₁

A:

Q: Try to guess a formula for f' (x) where f (x) = 2*. f' (x) =

A:

Q: State the interval of the function g(x) = E-x is %3D

A: The given function is gx=32-x  exist in the interval (-∞,32] and does not exist in any other…

Q: Consider the function f(x) = z + 6

A: Givenf(x)=1x+6

Q: For what x-value is the function y = |x+5| not differentiable?

A:

Q: Describe the domain of the function f(x, y) = ln(4 x - Y).

A: as per guideline i am answering one question .please give a like !

Q: Find values of x where the function is not differentiable f(x)=lx-2l+3

A:

Q: Differentiate the function with respect to the independent variable. f(x) = - 8x+ e + e f'(x) = D

A:

Q: 1 For what value of x does the function g(x) =x³ – 2x² concave downward? %3D

A: Consider the function  gx=13x3−2x2

Q: O For what value of x does the function f (x) = 4x2 – x +1 have a horizontal tangent?

A:

Q: 8. 4 2

A: In this question we will use basic of calculus i.e use of tangent function. We will write the…

Q: X+1 5) Is the function given by f(x) x2 - 8x + 15 continuous at x = 3? Why or why not?

A: f(x)=x+1x2-8x+15

Q: 6- For the function y=lnx a- Describe what type of function it is. b- How is the function related to…

A:

Q: Does knowing that a function ƒ(x) is differentiable at x = x0 tell you anything about the…

A: Does knowing that a function ƒ(x) is differentiable at x = x0 tell you anything about the…

Q: 14) What is the domain of the function f(x) E, ?

A:

Q: 1. Sketch the reciprocal of the function f (x) = x - 6.

A:

Q: Differentiate the function.

A: Given: y=ex1-ex

Q: he function f(x) = 5

A: Here we have to find the interval at which function f(x)=5x-ex is increasing.

Q: Solve the Problem. Approximate the curve of the given function f. f(x) = 2x3 – 18x?

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Find the curve length of the function 1 1. f(x) = ;x² 0 < x < 3

A: We can find the curve length as below.