Problem 2.1 (max, argmax, min, argmin) Let f(x) := (2+ sin(2.x)) and A := [0, 2]. (a) Compute: maxeA f(x) and argmax f(x). XEA (b) Compute: min,eg f(x) and argmin f(x). XEA Compute: argmax |[2 -e-f(x}+5 _ -가 (c) XEA (d) „Compute: argmin [11 – In (2 · f(x) + 5)].

Q: find the range of the following function f(x) = -2sin((x/2) - (pi/3)) + 5 ANSWER CHOICES a)…

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Q: 3/Describe using words the transformations that can be applied (in order) to the parent function to…

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Q: Evaluate the expression a+b a+b when a=23a=23 and b=45b=45. Write in simplest form

A: # the expressions are printed twice , taking them once given a=23 and b=45 The value of a+b is as…

Q: Differentiate the function f(x) = 7√x - 2. (Use symbolic notation and fractions where needed.) 7…

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Q: If f(x) = cos x + sin x, what is f"" (x)? 46 f""(x) = sinx- cos x f"" (x) = sin x + cos x o f(x) =…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: If f(x) = 3 – 4x, find f-(-17).

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Q: approximate sin(x) with case 1 1 case2 x case3 x^3 in two ranges (-1,1)

A: By using taylor series  sinx =x-x33!+x55!........

Q: Step 4 To find (f-l)'(x) use the theorem that states that if f is differentiable on an interval I…

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Q: Need help with number 2

A: we have to differentiate two times of f(x) ,where f(x) is given by

Q: Determine the domain and range of 1.) f-¹(x) = x-1/2 2.) f-¹(x) = x-4

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Q: If f is one-to-one and f( – 3) = 12, then f-'(12) and (f( – 3))¯

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

A: Here we use division rule of differenciation.

Q: Find the derivate of this function]: a) f(x)= 9x²³+24x² - T F'(x) = b) f(x) = 4x³ + 9x²-9. F'(x) =…

A: (a)  f(x)=9x3+24x2-πd dx(xn)=nxn-1d dx(constant)=0

Q: The percentage of female high school graduates who enrolled in college is given in the table below.…

A: Let x represent time(in years) since 1970, and let y represent the corresponding percentage of…

Q: Figure 5 shows f,f', and f". Determine which is which. (A) (B) (C) FIGURE 5

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Q: b) The difference of two real-valued functions f and is defined by f – g := f + const_1 · g. That…

A: b) We want to express the given definition of the function in terms of two indicator functions. Let…

Q: Show that the function f(x)=x^-4 +cos(-2x) is even, odd, or neither."

A: Given, f(x)= x^-4 +cos(-2x) f(x)= (1/x)4 + cos(-2x)

Q: Eketch a graph of the function f(x) = 5 sin ( 7x ) 3 6+ 5- 4- 3 -8 -7T -6T -5T -4T -3A -2T ST -2 -3…

A: Given, fx = 5sin13x  We have to sketch the graph of the function

Q: Suppose f and g are one-to-one functions such that f(2) = 7, f(4) = 2, and g(2) = 5. Find the value,…

A: We have given functions f and g are one-to-one. Then, a. gof-17=gf-17=g2=5 b. fog-15=fg-15=f2=7

Q: Composites of Functions

A: As per company guidelines, I can solve only first three subpart.

Q: 1.) f (x) = 10x10 4.) f (x) = %3D 2.) f(x) = x² – 9 5.) f(x) = 2x² + Vx 3.) f (x) = –x5 – x-3 – - x

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Q: 36- let gix).x-x and hlx)acosx find! 1- 3.

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Q: Identify the original function f(x) and what value of c to evaluate f'(c). (3x-9x²)+(42) x+2 lim…

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Q: Assume that f is a one-to-one function. (a) If f(6) = 2, find f-1(2). %3D (b) If f-(4) = -9, find…

A: One-to-one function means for every value of x, there will be a unique value of f(x).

Q: 4.) f (x) = %3D x3 5.) f (x) = 2x² + Vx

A: we have to find the differentiation of given function

Q: Determine the type of functions from R to R with necessary figure. i) f(x) = 5x + 7 ii) f(x) = (x² +…

A: (i) fx=5x+7 This function is state line and has roots is x=-75

Q: Plot the function f(x) = sin(x)cos(2x) and its derivative, both on the same plot, for 0<x<2n. Plot…

A: Given f(x) =sin2(x)cos(2x)⇒f'(x) =2sin(x)cos(x)cos(2x)-2sin2(x)sin(2x)

Q: It can be shown that for arbitrary b, 8(bx): 8(x) You can assume these results for this part of the…

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Q: F) y= 4x³ In(8x)

A: y=4x3ln8xd dx(xn)=nxn-1d dx(lnx)=1xd dx(ab)=b×dadx-a×db dxb2

Q: real mummber tzo ) if fex)= 20Vř, Show that for any f (t x) = VE +(a) 2) Consider the function fx)=…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.