Let g(x) = sin(x). Use Addition or Subtraction Formulas to show the following. g(x + h) − g(x) = (sin(h)) cos(x) – sin(x)(- 4 g(x + h) − g(x) h = sin(x + h) - sinch) h · cos(h) + cos(x) sin(h) - sin(x) h 1 = cos(h)) h sin(x) (1 cos(h)) 1 (sin(h)) cos(x) - sin(x)(¹ = cos(h))

Q: plot the function f(x)=x*sin(x)-cos(x) to show that it has one root at the interval [0,pi/2]

A: The given function is  defined in the closed interval .We shall fill the following tabular column.…

Q: Let f(æ) = sin(x) and g(æ) = x² . Find (go f)'(x) O 2sin(x)cos(x) O 2xcos(x?) -2æcos(x?) 2xcos(x)

A: Given that f(x)= sinx and g(x)=x2. And we find (g0f)'(x). We know that d(xn)/dx = nxn-1.     Here i…

Q: Differentiate the following functions using the quotient rule. a) You are given that f (x) a df dx…

A: The Power Rule:The Chain Rule:The Quotient Rule:

Q: A quick way to graph cos(x + h) – cos(x) is g(x) = lim h→0 h to graph which of the following?

A: Given that, gx=limh→0cosx+h-cosxh By definition of the derivative of a function fx is,…

Q: Let f(x) = sin2x and g(x) = cos2x. Determine whether h(x) is in span(j(x), g(x) ) h (x) = sin 2x

A: We have to determine whether the function hx=sin2x is in the span of the functions fx=sin2x and…

Q: Let f(x) = sin2x and g(x) = cos2x. Determine whether h(x) is in span(j(x), g(x) ) h(x) = cos 2x

A: Given  f(x) = sin2x, g(x) = cos2x and h(x) = cos2x Then, we have to determine h(x) is in span(f(x),…

Q: ) Define the domain and range of f(x) where f(x) = sin²(x) – 1

A: The function f(x)=sin^2(x)−1 is defined for all real numbers x because the sine function, sin(x), is…

Q: cos( – x) + tan( – x)sin( – 2)

A:

Q: g(æ) + x sin(g(x)) = x? – 25 and g(5) = 0, then g (5):

A:

Q: 4) a) Determine the simplified expression for the 623rd derivative for the function f(x) =cos(2x)…

A: a)   fx=cos2x+sin2π     =cos2x+0      = cos2x

Q: (2) Let f(x) = -3 sin (r +). (c) And then determine the domain and range of f(x).

A:

Q: Analyze and sketch the graph of f(x) = (cos x)/(1 + sin x).

A: Given function: Analyze and sketch a graph of the given function. first we make a table so get…

Q: ( (cos(2r) – sin(2x)cos(2x)) -dx =. For +C. What is F (x)? cos(x) – sin(x)

A:

Q: 2x sin-1(x²)dx =

A: This question is taken from the indefinite integral in which we have to choose the correct option…

Q: Consider the functions: f(x) = (cos(x) − sin(x))/cos(2x) and g(x) = 1/(cos(x) + sin(x)) where in…

A: cos(2x) = cos^2(x) - sin^2(x)

Q: Find a0 of the function f(x) = sin(x/2

A: Given function is:  fx=sinx2

Q: Let ƒ(x) = 4x − sin(4x). a) Find f (0). f(0) = b) Find ƒ(§). ƒ(§) = CHECK ANSWER

A: Given query is to find the value of the function at indicated points.