A. Bernoulli's Egquation 2. (3 tan X - 2 cos y) sec?xdx + tan x sin ydy - 0

Q: Parts D,E, and F

A:

Q: a. Express x = -3+52 in its trigonometric form r (cos(0) + i sin(0)) with 0 ≤ 0 < 2. Give your…

A: Given:  a) x=-3+5i Any complex number z=a+bi  has a trigonometric form  x=rcosθ+isinθ where…

Q: xpress tiIE SS the f (x) = 3 sin? x + cos? x of oog m

A:

Q: 1-2sin?x X. 36 – 4sin? xcos?x sin x cos x + C Arcsin 3 Arcsec sin 2x + C 1 Arcsin sin 2x +C 6 -글사 O…

A: To find the integral.

Q: (sin(t) + cos(t))² – (sin(t) – cos(t))? -- - Simplify to a single trig function 2 sin(2t)sec(t)

A:

Q: snip

A: We have been given the three functions such as  f(x)=sinx  -π2≤x≤π2g(x)=cos x  0≤x≤πh(x)=tanx…

Q: (e* – 1)? lim I-0 x sin x

A:

Q: y=sin x sec X , then y' = A O cos? x- sin? x B O sec x -csc x 1° D O

A: To find : y'

Q: snip

A: It is given that;  f(x)=sinx, -π2≤x≤π2,g(x)=cosx , 0≤x≤π,h(x)=tanx,   -π2≤x≤π2 We have to find the…

Q: 4 sin? r d) lim a-0 3x tanx

A: see below the answerHere we use the L'Hospital Rule islimx→af(x)g(x) is of the form 00 then…

Q: L1 {a/[S(S + a)]} = (A) a sin at (в) 1-е^at с) е^at (D) sin at

A:

Q: ·S- x² + sece tane de sece - 1 e integral sec²0 de 1+tan cose de 1-sin sine de S x dx can be…

A: The given integral is ∫x dxx2+x2-1-1. We have to change the integral using substitution.

Q: If y=tan(arcsec/x), then dy/dx is sec2(arcsec/x) A x-1 B 2(х- 1) x-1 2(x-1) sec-(arcsec/x) D 2x E…

A: Let's find.

Q: TC + (c) Given that In = tan" x dx , show that %3D In + In-2 = (n 2 2) %3D Hence, find 8. tan (2x)…

A: Given an integral : In=∫0π/4tannx dx We need to show : In+In-2=1n-1 , n≥2 Also we need to find…

Q: 7a/4 Evaluate the integral (sin x+ cos x) dx using the fundamental theorem of calculus. Discuss…

A:

Q: 2 cos? x – sin x – 1 = 0

A: We need to solve the equation 2cos2x-sinx-1=0.

Q: s2 L-1 (s² + a²)² 1 [sin at + at cos at] 2a

A: If the Laplace transform of a function f(t) be F(s), I, e L{f(t) }=F(s) then f(t) is called an…

Q: Sంబు ఒపా వింద ఇ + పిల్లయ 2-Sin LA Sin A tos A Sin A t cOS A 0.

A: Given : (2sin³A + 2cos³A)/(sinA + cosA) = 2 - sin2A

Q: m/s Let sin A = sin(A + B) cos(A + B): = tan(A + B) = with A in QII and sin B: X X X 8 - with B in…

A: Topic = Trigonometry As per guidelines, At a time only three sub-parts of a question can be…

Q: x = 3 sin 0 is an appropriate trigonometric substitution for the integral 3-x2 dxp. x2 Select one: O…

A:

Q: 4 sin(A) – cos(A) | If tan(A) = , then %3D %3D 4 sin(A) + cos(A)

A:

Q: |2x sec?x dx = Select one: O a. 2x tan x +2 In|sinx|+C O b. 2x tan x +2 In|cosx|+ C . C. 2x tan x -…

A:

Q: cos(In x) dx =? A 1/(sin 1) B sin 1 1/(cos 1) D sin(e)

A: Given integral can be evaluated as shown below

Q: 1 The function (x) = x sin x satisfies the following equation: f"(x) + (x) + t cosx = 0. The value…

A: Introduction :

Q: snip

A: Consider fx=sin x, gx=cos x. Evaluate: fg-1513. Let gx=y. y=cos x Replace y by x and x by y. x=cos…

Q: cos*x If S(cos3x B) dx = - + C, what is the B? 4 A. - sin x С. - COSX . 1 D. 1 В. CSC X sec x

A:

Q: e sin e Cos e tan 0 a 0.5446 0.2924 0.4452

A:

Q: 10. Evaluate. (d) sin-1() (e) sin¬1 (sin (7)) (f) sin- (cos (E) (a) sin-' (0) (b) cos-1 (-) (c)…

A:

Q: i1. L'[s/(s² +a)*]= (1/2a) t sin at 12, L' [1/(s² + a?)² = (1/2a) (sin at – at cos at) %3D

A: Introduction: The convolution is very significant in calculatig inverse Laplace transformation.…

Q: n(en sin-lx ) dx cos(sin -lx) +C Vī-x? 1–x2 A) True B False

A:

Q: S tan?x secs x dx 1 х + Ос none of the choices 1 -sec"x + sec*x + C + C O A B.

A:

Q: 4. f(x) if f(x) - In(sin?x cos?x) a. 4 tan 2x b. 2 tan 2x c. 4 cot 2x d. -4 cot 2x

A:

Q: 17. x= sin t and y = 2 – cos´ /

A: Given: x=sin ty=2-cos2t

Q: d (d) Compute (cosh(x)). dx (e) Compute cosh(x)+ sinh(x). (f) Show that the hyperbolic sine function…

A:

Q: If y=tan(arcsec /x), then dy/dx is sec?(arcsec/x) (B) none of the given choices x- 1 2(x– 1) 2(x- 1)…

A:

Q: x2 cos x 6. Find for y = ln: dx sec x а. 2x – sin x – tan x sec x b. + cot x - tan x 2 cot x – tan x…

A: We need to differentiate the equation with respect to x.

Q: 5. x = A sin (at + B); w a parameter, not to be eliminated.

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

Q: al Evalluate; I. cos X AX V sin x Hints sin'x+cosX-4

A:

Q: 5 35 sin? 0 cos50 de -2 S(x e* – tan x)dx -3

A: We are entitled to solve only one question at a time and up to 3 sub-parts only. Given - ∫0π235…

Q: HW: (1) Prove that: cos'e (a) 1- tan'e 1-cot' @ sin'e -1, (b) tan'0.cos' 0 + cot³ 0.sin³ 0 -1

A: The detailed solution is as follows below:

Q: #3. Sketch y = sin x and y = cos x for 0 < x< 2n. Locate the x-intercepts. sin x CoS X 1 37 37

A: X intercepts are values where the graph cuts the X-axis.

Q: 1%09 lIı. A bb a 1:1Y 2-tan a If sin(x + a) = 2 cos(x – a), then tan x 1-2 tan a' True False O Leave…

A:

Q: 6. What is value of y that is no y = sin-1 x? A. 0 С. B.

A: here we have to find the value of that is not in the range of the function y=sin-1x

Q: 6. sin A = cos A tan A

A:

Q: 0 ( -1 tan x du Q\ find dy if (xay sinx=(√√ au) - y² cosi'x

A: Given data:- x-ysinx=∫x2tan-1xdu1-u-y2cos-1x

Q: 5. y = cos" (cot (esc V?)| - 3x)' tan x (1 6. y = 5x2 - Vcsc x 7. 2x sin y = (2x + 3y)°

A:

Q: 20. A certain substitution gives S sin³x cos"x dx = S (u° - u’) du . What is n? Your answer

A:

Q: 9- x2 Consider using Trigonometric Substitution what is dx ? x2 3 sec e tan e de 3 sec e de 3 sec2 e…

A:

Q: sec x + coOS x dx 2 cos x

A: To evaluate

Q: cos 2x+sin? x 1.4 a) Prove the identity: =1- sin x. 1+ sin x

A: