sin x dy (1 + y) cos x + sin x If y=- , prove dx %3| cos x 1+2y + cos x- sin x 1+ sin x 1+ 1+ coS x 8

Q: x´ tanh x f (x)= tan -1 (x)%3Dtan 2 sin x+ coS X

A: This is a problem of Differential Calculus.

Q: * (D'+1)y(x) = tan(x) 1-sin(x) 1+sin(x) 1+cos(x) - y,(x) = sin(x)In m(x)s03 = (x) 2- -- y,(x) =…

A:

Q: Evaluate cos x+ 2 cos x+1 dx sin x sin x - 3 cos x cost x 7. +x+c 2 cos x +x+c 3 cos X- cos x (sin x…

A:

Q: cos x sin* x dx 2. [ cor'x sin'x de 1. 7/4 7/3 3. cos x sin x dx 4. /4 | cos³x sin³ x dx

A: According to our guidelines, we can answer only three subparts of a question. Other parts can be…

Q: f(x) 3 cos x 2 tan x - - f'(x) = f' 3 r()-

A:

Q: y" + y = 2 cos x – 2 sin x; y=x sin x + x cos x y" +y = sec x; y = x sin x + (cos x)In(cos .x)

A: We have two methods two check whether given function is solution of differential equation or not  i)…

Q: cos x ...ş gl x = 0 die f(x) = -( أن قيمة مشتقة الدالة ... ..... 1- sin x

A: We have to find the derivative of the given function    The given function is  f(x)=cos(x)1-sin(x)…

Q: 9) Find all relative extrema in the interval (0, 2π) for y = x - cos x

A: Here we have to find the relative extrema.

Q: sin 2n x Prove that: dx = 0 for all n e N. sin x

A:

Q: cos x dx sin x-3sin r+2 1-

A:

Q: 1 -dx cos.x-1 2) Integrate

A:

Q: ON 3 sec3(In x) + sec2(In x) tan(In x) 2х n x) tan(In x) n x) dx c³(In x) + sec²(In x)

A: We have to choose the correct option according to the given information

Q: lim h-0 2h sin(x² )dx = -2h cos(1) sin(1)

A:

Q: integral (x 2 + 2x ) cos x dx

A: The given integral is ∫x2+2xcosx dx. It is known that ∫udv=uv-∫vdu. Let u=x2+2x   and  dv=cosxdx.…

Q: 2 sin(x) cos(x) + v2 cos(x) = 0 COS

A:

Q: 1. If tan-1 x x 1’ f(x) = Then S(x) dx =?

A: This question is related to definite integration, We will solve it using given information.

Q: cos x + sin² x + 1 dx cos² x (sin² x + 1)

A:

Q: | sin“ x cos' x dx 4. Integrate:

A: Given: ∫sin14x cos5x dx  To find: Value of the integral.

Q: cOs x 1. S sin x (1 + cos x) ecosx dx

A:

Q: integral Scos 4 (3x) Sin (3x) dx Evaluate the

A:

Q: sinx+5* dy for y=In dx e3Xtan(x³) O a. Some other answer cosx+5*In5 3x²sec²(x³) - 3 tan(x³) b. dy dx…

A: We have given y=ln(sinx+5xe3xtan(x3)). Let us simplify right hand side using logarithmic…

Q: sin x dx 1- sin2 x 4. cos x dx 2+3 sin x 5.

A:

Q: sin x 8x y%3= 8x sin x dy COS X %3D COSX dy COS X 8. %3D 8. COS X dy O dx X COS X + sin x %3D 8 sin…

A:

Q: 1. f(x)= xsin x 2. f(x) = x?cos 2 x 3. f(x) = tan x – sec x sin x 4. f(x) =

A:

Q: sin(5x) dx 2+сos(5x) اخترأحد الخيارات х + tan(5x) + с.ао —In | 2 + сos(5ӕ) | +с.Ь 1 +c.c 2+сos(5ӕ)…

A: Since , in the given integration problem we have derivative of denominator in numerator so we will…

Q: S tan -) dx = a) x tan-1 (-) +÷In(x² + 1) + C b) x tan-1 () +글x2-글In(x2 + 1) + C c) x tan-1 (는) +글x2…

A:

Q: 2 (sin x cos x + x) + C - 2 (sin x cos x + x) + C (sin x cos x + x) + C -(sin x cos x + x) + C [(cos…

A:

Q: 4 points lim h→0 2h cos(x² + 1)dx O 1 O cos(1) O sin(1)

A:

Q: SV1+ sin2(x - 2). sin (x – 2). cos (x – 2) dx

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

Q: *y=(sin(x)+cos(x))cos(x). dyldx -sin 2(x)+cos*2(x)+2cos(x) -sin 2(x)+cos 2(x)-sin(2x) O

A:

Q: 1. f(x) = xsin x 2. f(x) = x²cos 2 x 3. f(x) = tan x – sec x sin x

A:

Q: x*sin (2x) dx a. ** cos(2x) – x³ sin(2x) –r² co. 3 x² cos(2x) +x sin(2x) +- cos(2x) + C 4 1 cos(2x)…

A:

Q: cos x In (1 + x) a) dx. b) lim 1 - cos x

A: Given: ∫011-cos xx2dx limx→0ln1+x21-cos x

Q: cos*(x)dx

A: According to integration reduction formula ∫cosn(x) dx=n-1n∫cosn-2(x) dx+cosn-1(x) sin (x)n . For…

Q: sin' x Evaluate : dx (1+cos x) 1+ cos x+ cos* x 1+ cos x)1+ cos x+cos cos' x

A:

Q: sin(bx)+a x<0 f(x)=< | sin (2x)+2x x20 which is differentiable everywhere, then what are values of a…

A:

Q: 6 x° cos(x) dx =. 6 x³ sin(x) + 18 x² cos(x) – 36 x sin(x) + 36 6 x³ sin(x) – 18 x² cos(x) – 36 x…

A: Integration by parts  ∫udv=uv-∫v.du

Q: sin x dy (2y Cosx + sin4 x) ax

A:

Q: 7) f(x) = sin² x+ cos² x %3D Cosx-Sin X Sin X Sinx t cosx

A: Given

Q: 5. (cos" x- y cos x) dr - (1 + sin x) dy =0

A:

Q: 2 *sinh“ x – sinh x+ cosh x dr -dx cosh¯ x

A:

Q: 3 sinx+cos x Evaluate S dx. 2 sinxcos x

A:

Q: sech x+csch x Q3: prove that e2x %3D csch x-sech x

A:

Q: 0sin 2 x coOS x dx

A:

Q: Integral of sin^4 (x/2) cos^2 (x/2 dx

A:

Q: sin x dy (1 + y) cos x + sin x If y=- , prove dx %3D cOS x 1+2y + cos x-sin x 1+ sin x 1+ 1+ cosx 8.…

A:

Q: sin (x) dx (2+3 cus(x))² 3(2+3 cos(x)) с

A:

Q: dy sin x Find in y = dx 1+ cos x 2 2 2 cosʻ x+ sin´ x+cos x cosʻ x+ sin´x а. b. (1+ cos x) (1+ cos…

A: Topic :- derivatives

Q: ( (cos (2x) – sin(2x) cos( 2x)) cos (x) – sin(x) For (x) +C. What is F (x)?

A:

Q: cos(2x)- sin(2x)cos(2x)) cos(x)- sin(x) dx = -F(x) + For C. What is F (x)? 3.

A: