- The general solution of the equation dy dx = (1 + y²) cos x is y(x) = tan(C + sin x). With the initial condition y (0) = 0 the solution y(x) = tan(sin x) is well behaved. But with y(0) = 1 the solution y(x) = tan (7 + sin x) has a ver- tical asymptote at x = sin(1/4) z 0.90334. Use Euler's method to verify this fact empirically. ) =ta

Q: If f(x)=2 sin x/1+cos x, then f′(x) =    f′(4) =

A: We have to find

Q: If f(x) = cos x – 7 tan æ, then f'(z) -sin( x ) – 7 sec²(x) = f'(2) =

A:

Q: T (8) If g(x) = sin(x) *cos(x) find g'(-).

A:

Q: 4sinx (x)cos (x)dx = (0) (b) () (d) (e) None 16

A:

Q: Solve the D. E. to the I. V. P. sinx(e- + 1)x' – cosx = 1, y(-) = 0 (1 + e") (1 – cos x) = 2 O (1 +…

A:

Q: (b) Find the five special points on the graph of y = f(x) in the first period.

A:

Q: on Find an equation for the function f(x) whose derivative is f'(x) = 4sin(8x) and whose graph…

A:

Q: (#6) S sin³ (x)dx =

A: Given  Rewrite  sin3x=  sin2x * sinx  Use Pythagorean identity sin2x + cos2x=1

Q: y (3, 4) sin(0) = %3D cos(0) = tan(0) = csc(0): sec(0) : cot(0) = %3!

A:

Q: Find the solution(s) of the equation sin (x + 1) = v2 cos e within the interval 0 < x < 27.

A:

Q: f(x) = cos(x) + 3 sin(x) +x Find the roots using secant using initial guess -0.1Y and 0 with an…

A:

Q: (b) S – cos(x) + 5 sec x cos x dx

A: This is is integration question

Q: (i). y' = 1 + 3y tanx Ans. 3y cos³x = c + 3sinx - sin³x

A: this is a linear differential equation. solve it using integrating factors.

Q: f ‴(x) = cos(x),    f(0) = 4,    f ′(0) = 6,    f ″(0) = 7 Find f.

A:

Q: Consider the following function. f(x) = 2 sin(x) + 2 cos(x), [0, 2n] Find f'(x). f'(x) Find f"(x).…

A:

Q: (b) f(z) = tan¯"(5z) - (In(2"))®

A: We have to find derivative

Q: (#5) ſ cos³ (x)sin*(x)dx =

A: Given the function,

Q: Given that f"(x) = cos(x), f'(x/2) = 4 and f(r/2) = 7 find: f' (x) = sinx+3 f(x) =

A:

Q: 2. Draw the graph z = - cos(y) for 0 < y < 2n, and then use it to help you sketch solutions of y' =…

A: Firstly we draw the graph of z=-cos(y) for the given interval. Then we find the critical points and…

Q: 47. Show that y = sin(tan-x+ C) is the general solution of y' = /1 – y²/(1+x²). Then use the…

A:

Q: Let f(x) -9x(sin(x) + cos(x)). Find the following: 1. f'(x) = -9x cos(x) +9x sin(x) – 9 sin(x)-9 cos…

A:

Q: In my example, f(x) and g(x) line up after 3 f-wavelengths, and 2 g-wavelengths. You've got to make…

A: 9 period of f(x) and 6 periods of g(x) before they both line up.

Q: #17 Determine the equations of function graphed below.

A: According to question We have to calculate the equation of the graph.

Q: If y = sin (sin x) and d dy tan x + f(x)= 0, then f(x) equals dx2 (A) sin² x sin (cos x) (C) cos? x…

A: Introduction :