Evaluate: +3) V1-x2 19. dx A. V1- x² + arcsin x + C C. - V1- x² +3arc cos x + C B. – V1- x² +3 arcsin x + C D. VI– x² + 3ln|1– x + V1- x² | +C

Q: 2. If f(x, y)=x² sin y-y cos.x-xe - ye" +5x°y°, show that ô²f _ ô²ƒ ôxôy ôyôx

A:

Q: Let ro)-플-x a-글 FW) = b = 0, and n=3. Then: cos (f(x))dx =

A: We can find the integration as below

Q: Q6:-Prove that: y" =1 y =csc(tan"") if

A: Given y=x4·csctan-114x2-1 Let tan-114x2-1=α ⇒tan(α)=14x2-1 ⇒cscα=2x ⇒y=x4cscα⇒y=x4(2x)⇒y=x22

Q: Prove that J5/2(x) = 2 TCX CScanned with CamScanner 3-x² 2 sin x - 3 COS X

A: Use the given information.

Q: Which is the du in y= sin (x2-2x + 1)? x2-2x + 1

A:

Q: = cos(x + y), when x = 0, y = " %3D

A:

Q: A particle moves in the xy-plane in such a way that its path is defined by x = et cos t and y = et…

A: Given that, x=etcost, y=etsin2t. Differentiate x with respect to t, dxdt=etcost-etsint=etcost-sint…

Q: Find Duf at P. 3 4 f (x, y) = sin(3x – 4y); P(4,3); u = i j %3D - - NOTE: Enter the exact answer.…

A:

Q: if y=tan x,prove that y'''=2(1+y²)(3+y²)

A:

Q: Differentiate with respect to x: y= In(3x2)/x3  and y=x2sinx/cos2x

A:

Q: 26. i) differentiate, with respect to x a) cos (2Vx) In(2x) b) 27. Differentiate y with respect to x…

A: See the attachment

Q: 8- Evaluate a) ſe² + 4 sin(8z) dz 1+9cos(8z) бх- х2 b) J 73-9x²+8 esc²) dx Csc2 - х3-9х2+8

A: We have to use proper substitutions.

Q: ze : use the Implicit Differentition to find ax 'ay 1) 3yz2 - e4* cos 4z - 3y2 = 4

A: 3yz2-e4xcos4z-3y2=4

Q: D[Expf-3x] Cos(nt], {x,2},t]

A: Correct option is D

Q: Use the Substitution Rule to provethat∫cos2ax dx =(x/2) +(sin(2ax)/4a) + C.

A: The given integral is ∫cos2axdx=x2+sin2ax4a+C

Q: Evaluate using the result of Exercise 54

A: Given: limh→0cos3h-1h2 we know that 1-cos2θ=2sin2θ…

Q: التاريخ اليوم موضوع الدرس A) Discuss the conrergence of facx) %3D on A = Co,0)

A: Convergence of the sequence

Q: d x 2. 1+xVI-(Tanin)

A:

Q: Q25: A = e-2x – 3x5,B = 2Vx, C = sin³ 3x + 1 find A"" + B" - C'. (а) —8е-2х --sin 3x sin 6x – 180x?…

A:

Q: GIVEN: f:0,2x]- -R, f(1) = sinz+ cos I %3D Find f (x) in factored form.

A: Differentiate the function fx with respect to x.

Q: (b) Show that U (x, y) = eu cos v, V(x, y) = eusin v are conjugate harmonic of each other if f = u +…

A: It is given that,  f = u+iv  is analytic. We have to show that,  U(x, y) = eu cos v  and  V(x, y) =…

Q: O i using The( 3) uence Xm>is

A: First we have to show that Given sequence is monotonic and bounded then it is convergent

Q: If y = tan x, prove that y``= 2(1+y² )(3+ y²).

A:

Q: Q2 Q2/If y = (x³ + 5x² + 1)3 + Jsin+/cos³Vtan3x2 find y'

A:

Q: a2f Compute Je Je дх' ду f(x, y)= x²y² – sin 2 + xe" and : дхду

A:

Q: dy Find if y = 5x² sin4x dr' O None -20x? cos4x – 10xsin4x 20x? cos4x + 10xsin4x O 10x? cos4x +…

A:

Q: (12,50 Puanlar) 3- Evaluate the integral 3x +2 dx. V5 - 22 a) – 2 arcsin V5a + 3/5- a? +C b)2…

A: Given: The integral is ∫3x+25-x2dx

Q: A force of F(x)=x²-cos(3x) +2, x is in meters, acts on an object. What is the work required to move…

A: Given force f(x)=x2-cos(3x)+2

Q: by implicit di f foretiation of sin-(xy) - cos-(x- y) Find -V1- (xy)? xV1-(x- y) ² + V1- (xy)? -V1-…

A: Using Implicit Differentiation

Q: If y= tan x , prove that y`= 2(1+ y² )(3+ y²).

A:

Q: Find the general soultion of the follwoing equations dy cos x + y = cos²x, 15

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Obtain the general solution of 4dx = xVx² – 4dy. Express your answer in terms of cos function

A: The general solution of an ordinary differential equation is the an expression for the dependent…

Q: Find , if z= cos(3x² + 7y°) O 2x sin(3a? + 7y³) sin(3x² + 7y³) -9x cos(3x2 + 7y°) -6x sin(3x? + 7y°)

A:

Q: Show that U(,y) is Harmonic function and find its conjugate for U(x, y) = 2x – x³ + 3xy² -

A:

Q: Q4 Evaluate: f(1- cos²4x) sin4x dx.

A: The given integral is: I=∫1-cos24xsin4xdx   As we know the Power rule. ∫xndx=xn+1n+1+C

Q: • Find a harmonic conjugate of u(r, y) = x² – 2x – y². Show that u(r, y) = e" cos y is harmonic.

A:

Q: 2.2 Use the definitions of hyperbolic functions to solve for A and B if: 5e* - 4e* Asinh x+B coshx…

A: Consider the following equation:…

Q: Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y(pi/8) = 0…

A:

Q: Suppose f(x) =sin(3x- 2). Evaluate: A -3cos(3x- 2) +C B ® --cos( 3x – 2) +C © ;cos(3x – 2) + C D D…

A: Topic = Integration Correct option = B

Q: Obtain the approximate answer for 2 cos(x )dx using the trapezoidal method so 3) that the maximum…

A:

Q: ,In sec²(sin2y)dy can be evaluated by writing it as sec2y ! / sec²( sin2y) - 2 cos2ydy S. | sec2(…

A: To simplify the given integral.

Q: Q6:-Prove that: y" = 1 y =csc(tan"" ) if

A:

Q: B) f(x) = x+3 (-6, 6<x<1 Is f cont. at x-6?

A:

Q: Q25: A = e-2x – 3x5,B = 2Vx, C = sin³ 3x + find A" + B" – C'. - (а) —8e-2х sin 3x sin 6x – 180x? 1 1…

A:

Q: For u = ex cos y,(a) verify that ∂2u/∂x∂y = ∂2u/∂y∂x;(b) verify that ∂2u/∂x2 + ∂2u/∂y2 = 0.

A: The given  function is, u=excosy (a) To verify ∂2u∂x∂y=∂2u∂y∂x Solution: We have u=excosy…

Q: Q1/ Sketch x1[n] , x2[n] , x3[n] where : x1[n] =Sin(rtn) , x2[n]= e^( n), x3[n]=x1[n] - x2[n]

A: Graph of sin(πn)

Q: Which of the following are the solutions of tan²x+ secx = 1 on the interval [0, 2n)? %3D 2я 4я 3' 3…

A: for a quadratic equation ax2+bx+c=0 x=-b±b2-4ac2a

Q: Find the convolution of fix) = sin bx, g(x) = exp(-alx), a>0.

A: Convolution: Let and be two piecewise functions, then the convolution of them is denoted and defined…