Find all values of x that satisfy the equation f'(x) = g'(x) if f(x)=sin x and g(x)=cos x. a. * +kT, where k is an integer 4 O b. x = 4 + kTT, where k is an integer x = +kT, where k is an integer 3 O d. x = +k T, where k is an integer

Q: The maximum value of F in F(x) = - 4 cos x is 2 4 1

A: We know range of cosine function is [-1,1] Therefore maximum value of f(x)= -4cosx is, f(x)=-4cosx…

Q: Evaluate 1 70 sin° (f (x)) cos*(f (x))g(x) dx COS where g'(x) = r for all x with g(0) = T , • f'(x)…

A:

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: Find f. f "(x) = 7 + cos(x), f(0) = -1, f(71/2) = 0 %3D %3D

A:

Q: Suppose (=/3) = 3 and f '(m/3) = -7, and let g(x) = f(x) sinx and h(x) = (cos x)/(x). Find the…

A: So, Again, if , Then

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: The function f(x) = a sin x + b cos x + c satisfies f"(x) = cos x – 2 sin x, f'(0) = f(0) = 2. Find…

A: a=2 b=-1 c=3

Q: Describe with a sketch the end behavior of f(x) = cos x.

A: Given:            f(x) = cos x  The cosine function oscillates between values -1, 1 as x→∞ Hence it…

Q: f(x) = 10 sin x + 9 cos x f'(x) = %3D %D

A:

Q: Find f. f"(x) = 5e* – 8 sin(x), f(0) = 3, = 0 %3D %3D f(x) = IN

A: Answer and explanation is given below

Q: Suppose f(pi/3) = 5 and f'(pi/3) = -7, and let g(x) = f(x

A:

Q: a) Find a function f so that f’(x) = 6x + cos(x). b) Find a function g with g’(x) = f’(x)

A:

Q: Find f if f"(x) = 2 + cos(x), f(0) = -9, f(pi/2)=9 f(x) =

A: Solution of given question is followed by:

Q: Given that f (x) = 3 cos ⁡( x ) − 7 x + 4, evaluate f'(0)

A: f(x)=3cos(x)-7x+4 Note: derivative of cos(x) is -sin(x) and d/dx (x^n)= nx^(n-1) Use the above…

Q: Find all xE[0,2pi] that satisfy sin 2x + cos x = 0 x =

A: Topic- Trigonometric Equations We are given, sin(2x)+cos(x)=0 and x∈[0,2π] We know that sin(2x)=2sin…

Q: Are fi (x) = x, f2(x) = x², and f3(x) = 4x – 8x2 linearly independent or linearly dependent on (-00,…

A: Definition: A set of vectors are said to be linearly independent, if no vector can be represented as…

Q: Show that the function f(x)= x^3 − 15 cos(pi x) + 1 has three zeros in the interval [−4, 4]. Do not…

A:

Q: Find f if f"(x) =2 + cos(x), f(0) = 10, f(t/2) = -5. f(x) = |

A: To find f if f"x=2+cosx, f0=10, fπ2=-5. Solution: We have, f"x=2+cosx Integrating both sides, we get…

Q: Find f if f"(x) = 2 + cos(x), f(0) = -10, f(x/2) = 4. %D %3D f(x) = iii

A: Recall: ∫xn dx= xn+1n+1+c; where c is an integration constant. ∫sinx dx= - cos(x)+c; where c is an…

Q: Let f(x) = 3 cos 2x + sin² x. a) b) Show that f'(x) = -5 sin 2x. Зл In the interval <x< one normal…

A:

Q: Differentiate the functions. a) f(x) = 2 – 5x + b) f(x) = e* + cosx c) f(x) = d) f(x) = (5 – x²)· e*

A: Suppose f and g are differentiable function .Then note the following results : The power rule of…

Q: Find f. f"(e) = sin(e) + cos(e), f(0) = 5, f(0) = 4

A: f''(θ)=sin(θ)+cos(θ)Integrate with respect to θf'(θ)=∫sin(θ)+cos(θ) dθ f'(θ) =-cos(θ)+sin(θ)+C1Again…

Q: Linearize f(x) = 5 cos x about x = pi over 2. f(x) = -5x

A: linearization around x=a is given by :L(x)=f(a)+f'(a)(x-a)