sin (x) -1 5. h(x)= %3D 1+x

Q: x²-4 1) lim х>2 х-2 sin 2x 2) lim x→0 3) lim( X→0`x 5x2-Зх 4) lim X→∞ 7x2+1 d 5) [In|sin x|] - dx d…

A:

Q: [1+sin x) 'cos x dx (sin x)4 +C A ) x+ sin x + B -(1+ sin x)*+C (sin x)4 -+C 4 sin x +

A: Substitute, 1 + sin(x) = t

Q: z = sin-1(x/y)

A: z=sin-1xy Now, partially differentiate the function with respect to x and y. zx=∂∂xsin-1xy=11-xy2∂ ∂…

Q: dx sinh x - cosh x

A: To Evaluate: ∫dxsinhx-coshx Concept: i. ∫afxdx=a∫fxdxii. ∫exdx=ex+C

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: y- y' cos x = y² cos x (1 - sin x)

A:

Q: ropriate substitution, n³ (4x)cos*(4x)dx is equal to

A:

Q: sin (2x) dx (x²+L)(x-3) 3) (sin (2x) 88

A: We solve by Contour integration.

Q: 3 sin (x) 4- V1-x2

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

Q: 2 sin(-2 x) lim ثم أختر الاجابة ال 0.3) d x-0 4 sin (5 x)

A:

Q: S (sin'x-sinx-x' sin* x+x²sin x) dx ? :-x° sin* x + x² sin x) dx ? What is the value of the…

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: e2x - e 2x 3. lim, 0 sinx

A: To evaluate the given limit.limx→0 e2x-e-2xsin x

Q: sinh? (e-") 4. dx Cosh(e-x ex

A:

Q: 2х -3 -dx. Evaluate(x-2)(x² + 1)

A:

Q: Evaluate the limit.

A: Given that, limh→0sin(2h)(1-cos h)h2 Because of the direct substitution of h = 0 into this, we get…

Q: sinh x + 10 et cosh x + da e2x 2 100 + sinh? (100

A:

Q: integration of e^x(9-e^x)^1/2

A: Given that

Q: evaluate using the suggested method.

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: (sin (x))2 dx V1-x2

A: The given integral is

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: sin? 6, determine a reduction formula for the 5 By the substitution x = integral 2(1- x)2 dx. Hence…

A:

Q: (x²–1)dx S (x++3x² +1)[tan-1 x2-1 aluation of is

A: Given integral is I=∫x2-1x4+3x2+1tan-1x2+1xdx To evaluate I Now, dividing the numerator and…

Q: sin 2x J-1 x* +x* – x² +2

A: Here we have to find the integration: ∫−11sin2xx8+x4−x2+2dx

Q: solving (2 x sinxy+x^2 ycos xy ) dx + X^3 cos x y dy = 0

A: given the expression is ; [xsin(xy)+x2ycos(xy) ] dx + x3cos(xy) dy =0

Q: sinh-1x = In (x + vx² + 1) %3D

A:

Q: 10. lim ) 1 -1) A-0 hV1+h sin x 13. lim 0 2x-xr V8+x -2 (Hі 16. lim

A: We have to use proper techniques here.

Q: sin-1(e* 2 lim V1 - e2x x→0-

A:

Q: e*sin³ (=) e*sin³ 3 (t 3 x23 sech (x-2) xº sech (x-2) F (x) = S f(x), if x 2

A: Given that  gx=exsin3πxx2sechx-23if x≤20if x>2 Find the left hand limit of the function at x=2.…

Q: cosh-1 x dx CO: хах

A: Let the given integral be y - y = ∫cosh-1x dx y = ∫cosh-1x1 dxIntegrating by parts - y =…

Q: sin x dx + x cos² x 5.

A: Integral of a function is the anti derivative of the function, meaning area of the graph of the…

Q: h 1 lim h→0 2h sin(x² + 1)dx = -h

A: Here we will find out the required limit.

Q: x' cos“ x sin x dx. (л- Злх + 3х Evaluate: | -

A: For the solution of the problem follow the next steps.

Q: e2x+Inx² sin x² dx -+fe²x cos x² dx

A: This is a problem related to integration. Based on the general formula we will solve the problem.

Q: 0sin 2 x coOS x dx

A:

Q: solve eYsin(x) -y'cos"x = 0 2. cos¯x=0

A:

Q: f(x) = 8 cos x- 8 sin x f'(x) = %3D

A: Given function is fx=8cosx-8sinx.

Q: S sec³ x+esin sec x - dx

A:

Q: sin(x) * x - lerror| < 0.0000001)

A:

Q: ∫ln a/x sin^-1x dx

A: Given,           I=∫ln(ax).sin-1(x) dx To solve this integration we apply integration by parts…

Q: f(x) = e-x (3.2 sin(x) - 0.5 cos(x))

A: Here a simple python script written follow that.

Q: cosh 3 хр. 15) 1-sinh 3

A: Solution

Q: [sin x cos“ x dx 14 4. Integrate:

A:

Q: sin 2x J-1 x8 +x* – x² +2

A: Evalute the integration ∫-11sin2xx8+x4-x2+2dx.

Q: 13. y = - cos (x)

A:

Q: e-* cos² x (x + 1)2

A:

Q: sin x -dx = 5. 2- cos x A. – In(2) В. — Iin(3) c. In(3) D. 1-In(3) Е. In (3)-1 С.

A: Given: The integral  ∫0πsinx2-cosxdx

Q: . (sin a+ cos x) dy + cos x- sin x) de = 0. (Ans. y + log | sin x+ cos x|c)

A: Formulae used: ddxsinx=cosxddxcosx=-sinx∫1dx=x+c∫1xdx=log|x|+c