46. Given: RU || ST; LR = LT Prove: RS || UT U R 4 3 T S

Q: ủ (u x) = 0 for all u, v in R.

A: We will prove whether this is true or false as following.

Q: f"(1) = 4 - 6/1* f(1) = 6, f'(2) = 9, 1>0

A:

Q: Find u. (v x w). u = i v = j w = k

A:

Q: What are the endpoints of the latus rectum of (x + 1) = -8 (y + 4) ? O (-1 ± 4, –6) O (-6 ±4, –1) O…

A: We will find the end points of latus rectum as shown below

Q: v dA , R is bounded by r= 2– cose R

A:

Q: Is the following statement correct? The differential equation y' = (x² + y²)z has a unique solution…

A:

Q: dx 9) Which is equal to ? 1+e* A. x+ inh + e*|+C x-mh + * + C C. iml + *" -x+C D. Inh -e*|-x+C В. х…

A: solution is given below

Q: 4. a B A(0,e) B( = /2, 1/2) 7 ((0,1) Find the hyperbolic lengths a, b, and c. a Find coshlal cash…

A: Given: The points: A0,e, B12,12, C0,1.   (4.) To Find: The hyperbolic lengths a, b and c. (5.) (a.)…

Q: 6. Given: ZP=ZR; ZQ= ZS Prove: PO| RS P. 'R

A: ∠P≅∠R,∠Q≅∠S

Q: Which is always TRUE when AABC-AXYZ? m<A = m/Z O Option 1 Option 2 m/B = m/X

A: The solution is given in the next step.

Q: I. Use the composite midpocht rulo to approximate. 2 a) Sendox - For all 4 b) (3x ² √ x² +1 dx thuce…

A: Let h=b−an then the mid point rule is given by ∫abf(x)=h∑i=0nf(xi).Here, xi=xi−1+xi+12 is the mid…

Q: In r dy If y , then is cosh z

A: Straightway proceed to differentiate both sides,

Q: Prove that: V- A = -VA

A:

Q: Under a change of variables z = u°/3, y = v²/2 , the infinitesimal element of area dædy becomes 6uv…

A:

Q: 7 Prove : id Is perpendicular line to ra duic at its outer end point ,then t ang ent to the cirde is

A:

Q: 3. Find (ð v/ôx)x,z if v =x +y²-e²+ sin t and x+y=t

A: Given that  v=x+y2-ez+sint where t is given by x+y=t. So our function v becomes…

Q: 49. If f(u, v, w) is differentiable and u = x – y, v = y – z, and w = z – x, show that af af ду af…

A: Given f(u,v,w) is differentiable. By chain rule of differentiation , we have

Q: 35. Apply the convolution theorem to show that 2e Meu² du = e'erfvi. | (s – 1. (Suggestion:…

A:

Q: Q3. If w = f(u, v) , u = cosx and v = sinx, show that: d?w v² funu + u? fov – 2uvfuv – ufu – vfp %3D…

A:

Q: Finel the Laplace Trans Form 21 Ans. F(s)= 2(1-e ") 11)

A:

Q: 2 Evaluate the following contour integral ez $21-3 |2|=3 2(2-2) 3dz,

A:

Q: Ex 15: Prove that : d du a) tanh u = sech² u dx dx

A:

Q: cos? x dx x2 ex 3) Find the integrals if there exist i) Sozdx , ii) x2

A:

Q: O) Lind dyldx of 3 xex 1o X +3y = 0 2sinx cos y =1 9 x = sec 'y (2)

A:

Q: üx (u x i) = 0 for all u, v in R.

A: we have to identify the given statement is true or false

Q: Calculate 1₁ ₁² ² a feas = e¯² ds for the piece of the cylinder x² + y² = 16 for 0 ≤ z ≤ 7.

A: we have to find the ∬Se-zdS for the piece of the cylinder x2+y2=16 for 0≤z≤7