In Problems 43–48, use the figures to evaluate each function if f(x) = sin x, g(x) = cos x, and h (x) = tan x. 43. f(a + B) 44. g(a + B) 45. g(a - B) 46. f(a - B) x2 + y2 = 4 x2 + y2 = 1 (x, 1) 47. h (a + B) 48. h(a – B) I. Duoblanus đ0 74 astablich agal, idautitu

Q: If the general solution of the equation y" +9y = tan3x is expressed as y = f(x)sin2x + g(x)cos2x ,…

A: Given - If the general solution of the equation y'' + 9y = tan3x is expressed as y = fx sin2x + gx…

Q: Find the exact value. In 3 0 ³ sech 4 x tanh x dx

A:

Q: a if y = In (sinh 50) and x = 7. cosh 40

A: We have given y and x and we have to find out dy/dx

Q: if f(x)=ln(1+cosx) then find f`(x)

A: f'(x)=(1+cos(x))'/(1+cos(x))      =-sin(x)/(1+cos(x))

Q: 5 dr dy Suppose x and y are functions of a third variable t. If sin²(x) + cos²(y)=- and dr - 2, what…

A:

Q: Problem 2. Suppose that f (x) is a function that is continuous on the interval [-3, 3]. The graph of…

A: As per the instruction, we will be answering only question 2. Given: For (a), From the given…

Q: What do the limits limh→0((sin h)/h) and limh→0((cos h - 1)/h) have to do with the derivatives of…

A:

Q: -1 We can conclude from the derivative of sin-1(x)and cos-1(x) that sin-(x) + cos¯(x) is constant.…

A: Explanation: find the derivative of sin-1x & cos-1x

Q: two friends are trying to figure out how many supernova explosions there will be by looking at the…

A: The given function is fx=sin2x-cos2x-1 Convert sin and cos into the single function of sin…

Q: # 22 The weekly demand for propane gas (in 1000s of gallons) from a particular facility is an ry X…

A: The probability distribution function is f(x)=21-1x2; for 1≤x≤2 and 0 otherwise. So in the graph of…

Q: 1 Evaluate [ (x³ +cos(3x))dx 2

A: The given integral is ∫x3+12cos3xdx.

Q: 9. If f (x) = sin 3x so lim f(x+2h)+f(x-2h)-2f(x) ... -18h2 А. —3 sin 3x В. —2 sin 3x C. sin 3x D. 2…

A:

Q: 6. Suppose you wish to differentiate g(x) = sin²(x)+cos²(x). What is the fastest way to do this, and…

A: Given,

Q: 1) If y = (x-a)√2ax-x² + + a is constant. x- -1(*-ª) ,then y' = 2√2ax - x² a² sin-¹ a²

A:

Q: 9. If y = costhen the second derivative is 5x 25 Cos, 16 5x 5x sin- 4 d. 25 5x sin- 4 a. 25 b. C -25…

A:

Q: 3. Compute 4 (sin? x + cos? x) without using the derivative formulas for sin x and cos x.

A: Given:

Q: Find L{(t- 1) (2 - 5 sin 3t)}. 15 30s s2+9 (s²+9)? 2 15 15 s2 (s²+9) s(s² +9) 15 15 3-号- 3? (s²–9)…

A:

Q: Problem 2. Suppose that f (x) is a function that is continuous on the interval [-3, 3]. The graph of…

A: This question is based on application of Derivative.

Q: In this problem, please evaluate the trig functions without a calculator and de tion of the tangent…

A:

Q: Problem 5  Find the derivative of the following function using the Fundamental Theorem of Calculus.…

A:

Q: Use the definition of a derivative to find f'(x) and f"(x), when f(x) = 2/x. I got f'(x) = -2/x2,…

A:

Q: In Problems 47–58, use a calculator to solve each equation on the interval 0 … u 6 2p. Round answers…

A: Since you have posted multiple problems we solve the first three for you . To get the complete…

Q: If f(x)=tanh^-1 square root x to the fourth power then f'(x)=

A:

Q: 2. Evaluate: S(cos x)(In sin x)dx A. sin x (1 – In sin x) + C C. sin x(In sin x – 1)

A:

Q: 1. Suppose that the revenue (in dollars) from the sale of x units of a certain product is given by…

A: The revenue function is given by Rx = 70x-0.05x2 To evaluate: The expression of R'(x) using the…

Q: 5. Given b(x) = (3x – 7)*, if m(x) = 36 (2 tan-1 (1 – 7x)) then m' (x) is %3D %3D

A:

Q: 5. The function f(0) = (sin O+cos 0) + (sin 0– cos 0) may be written as

A:

Q: If G= ex Cos y log z + exyz Cos(xyz) Tan y - log (Cos x3) solve ∂3G/∂x2z

A: Given, G=excosylogz+exyzcos(xyz)tany-log(cosx3)

Q: What is the derivative of y = 10sin 5x 5 In 10 cos x 10in 5x 5 In10 (10sin Sx) A. C. 5 cos x In 10…

A:

Q: If f (x) = - cos(x), then f (10) (x) is equal to (A) - sin (x) ® -cos(x) © sin(x) D cos(x)

A:

Q: Let f(x), g(x) and h(x) be the functions from Problem A.1. Find the derivative of the following…

A: Recall:  Product Rule:   d dxf(x).g(x)=f(x).g'(x)+g(x).f'(x)   Given, derivative(x) = f(x) . g(x) +…

Q: Problem 6 Evaluate the indefinite integral.  ∫sec^6(x)tan^12(x)dx=_________________ +C

A: Let us assume that

Q: 5. Find all x-values in which your function has horizontal tangent lines, f(x) = 2 sin x + x. given…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 4) If y = 2√x - 2 tan-¹ √x, then y y' = -1 1+x²

A: Given :y=2x-2tan-1x

Q: 7. Find the derivative with respect to x of tan-(2) – In(2.r +3) = 4 cos (2y +5). %3D

A: To find the derivative of tan-1x2-ln2x+3=4cos32y+5. Solution: Power rule of differentiation states…

Q: 1) If f(x)= tan(5x), find  f'(5)=??????

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: 35) y = -4 sin x 4+ 2+ 2n -2+ -4-

A:

Q: 3. Use Simpson's rule to calculate x² sin x dx to within 2 × 10-5 of the exact value.

A:

Q: 3) If y = sin(2n), and x = cos(2n)

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: Find the extreme value/s of f(x) = 4 sin² x − cos 2x on . (³347) 3π 5π 2' 2

A:

Q: 17. Evaluate f-3x cos 2x dx a. --cos 2x - 3xsin 2x + C b. -cos 2x -sin 2x + C C. -cos 2x -³x sin 3x…

A:

Q: Example 1 Differentiate each of (a) f (x) =2 x' cosh x sinh t (b) h(t)=

A:

Q: Evaluate ax xm-1 sin bx dx in terms of Gamma function. -ax

A: We use the special results of Gamma function to solve this problem as in next step.

Q: 5. Find the PARTICULAR SOLUTION: y' = 1+ 3y tan x when x = 0 ; y = 1

A:

Q: Problem 1: Consider some arbitrary function f(x), whose value and whose derivative values of every…

A: The following concepts are used to analyse the linear approximation of the function. The graph of a…

Q: Problem 7. Let f(x) = -2x* cos(x) f'(x) =| %3D

A: The answer is