After getting a job, Kessy started saving a percentage of her annual income, which can be modeled by P(t) = 5.2 cos (0.517t) + 2.5, where P(t) is the percentage of her annual income that she was able to save on year t after she got a job. What percentage of her annual income did she save on the 4th year? *

Q: The lowest point on the graph of y = cos x, 0sxs21, occurs when x=

A:

Q: d Using the Chain Rule Twice Calculate 1+ Vx2 + 1. dx

A: Given function is 1+x2+1

Q: = - 1) ex²-x dx x. Use the substitution method to rewrite the function in the integrand, (18x – 1)…

A:

Q: 7. S(2 + tanx)²dx

A:

Q: -sinh(x) at x = 0 is dx21 Answer:

A: Derivative of the function

Q: by s-differentiation find L (t cos3t) = %3D s2 (s² +9) s2-3 .b O (s2+3)2 s2 (s²+9)2 s2-9 (s2+9)2

A:

Q: V3 B) If sinh 0 Find cosh 0, tanh 0, coth 0. %3D 2

A: We are given with sinhθ=32. We need to find some other trigonometric functions. Use the relation…

Q: Evaluate ]e * cos (7x) dx. Seex cos (7x) dx = %3D

A: Explanation of the answer is as follows

Q: B- Find dy / dx for the following functions: (3 mark) * 1- Y= sin( coshx log, 2 )

A:

Q: 4 dx. x'V16-x (c) By using x= 4sin (0), find

A: We have to find integration by substitution

Q: Q2/Find dx of y = sin(e') + xtan-1x. %3D

A:

Q: Consider the function y = sinh 2x + 1. Which ?one is a critical number of this function

A:

Q: use the chain rule to find: 28) dv 2- COSxy + y cos x

A: Solution:Given   z= cos xy+ y cos xx=u2+v and y=u-v2To find :dzdvFormula:ddx(cos x)=-sin…

Q: d²y nd by implicit differentiation if 3x² – 7y? = 14. dx?

A:

Q: Consider the following. 8x - 7x - 1 y = 3-x Find the value of y when x = 1. y(1) = Find dx dy dx dy…

A:

Q: solve using reduction of order (D^2+1)y=tanx

A:

Q: dy Q1: Solve the DE x3 dx3 +x = x Inx cos(2lnx) by using inverse dx operator method.

A: Given differential equation is .....1 Its solution is given by yx=C.S + P.I ; where C.S is…

Q: S sec x dx Use Integration by parts to solve

A:

Q: 2*csch( 2*) d x cosh(2*)-sinh(2*)

A:

Q: ÿ + ỷ = sec t tan t

A: This is the question of the differential equation.

Q: (5tan28 etan 28 sec² 2 Bd B

A:

Q: Integrate the function. 8 dx V36 - 64x2 X+ C sin-1 + C -1 + C D 4 tan-1 3. B

A: Given:       ∫836-64x2dx  substitute u=4x3→dudx=43                   dx=34du         =∫636-36u2du…

Q: Find one root of the equation below f(x) = cosx – x %3D using HIM and SECANT method of x = 0 and x =…

A:

Q: Find cosh² (t) sinh5 (t) dt.

A:

Q: Let y tan(5 7) Find the differential dy when x = 3 and da 0.4 Preview 3 and da 0.8 Find the…

A: Given function:

Q: c) Use trigonometric substitution to integrate dx 4-x2

A:

Q: Calculate the higher derivative. (Use symbolic notation and fractions where needed.) d? 8 cos (1) =…

A: To find,  d2 dt28 cos2(t)

Q: solve using variation of parameters or reduction of order. (D2 + 1) y = tan x

A: Given (D2 + 1) y = tan x

Q: f cos² x dx

A:

Q: . Estimate the root of the expression, f (x) = x² – cos x, using: d. MOSS using xo = -1 with error…

A: As per the question we have to find the root of the equation : f(x) = x2 - cos(x) = 0 With tolerance…

Q: Find dy/dx of y=1/ (tan-1 x)

A: The given function is: y=1tan-1x

Q: Q3: Find value of x if 3 cosh x- sinh x= 4

A:

Q: Find the function y = f(x) whose graph passes through the point (5π/12,3.5)if dy/dx =cos(2x−π/3).

A:

Q: 2. Use the identity of inverse hyperbolic function to solve cosh-(2 – a2) = ln 2, for |æ| < 1.

A:

Q: Q2- Find for the following function :- dx 1- y = sinh-(tan x) – tanh-1(sin x)

A: We will differentiate using direct formula and chain rule.

Q: dx (Solve it using integration by Rational fractions) sintx+cos4x

A:

Q: Evaluate the implicit function by finding dy/dx of x³+3y=3xy

A:

Q: What is the process for finding dy/dx when y is an implicit function of x? Illustrate with an…

A:

Q: 1) For #31-34, evaluate each derivative. d 3 dx ' sec /a* dx d. | ytan tdt dx

A: As per the company guidelines we can solve first three parts . I hope that the given solution will…

Q: d21 0 is sinh(a) dx21 at x = 0 is

A:

Q: f sin-¹(x) dx

A:

Q: 8x Find the average rate of change of f from 0 to 3 f(x) = sin

A:

Q: Use the trapezoidal rule withn= 4 to approximate cos(x) dx Keep at least 2 decimal places accuracy…

A:

Q: Q2) Find the derivative of the function at Po in the directi g(x, y) = x – (y²/x) + V3 sec-' (2xy),…

A:

Q: A typical adult human heart contains about 120 milliliters of blood when full (just before…

A: A sinusoidal function is a function that is a sine or cosine function and has repeating values of…

Q: Using Newton-Raphson Method, estimate the root (6 decimal places) of the following: f(x) = 3x-e cos…

A: The newton-Raphson formula for the roots is given by xi+1=xi+f(xi)f'(xi), where x is the root of the…

Q: 2. Solve the ODE using Separation of Variables. dy dx 5x²+4 y+1

A:

Q: alue of A can be calculated based on f(x)dx = 1.

A: The given probability distribution function is,