X1+iy,=X2+iy2" ューx,○ X =X ,=y,O *ュ=ソ,○

Q: Explain Clairaut’s Theorem.

A: Clairaut's formula for the acceleration due to gravity g on the surface of a spheroid at latitude φ,…

Q: Evaluate the integral dz 9 181- x² J81- x² 9

A: Given ∫09∫081-x2∫081-x2dzdydx

Q: Prove fulay's formule -CstD)4isin LO)

A:

Q: Prove Taylor's theorem.

A: The objective is to prove Taylor's theorem. According to Taylor's theorem we have, If fx be a…

Q: Use the Karl weierstrass substitution to integrate

A:

Q: Stoke's theorem

A: We have to verify the Stoke's theorem for the given vector field. It is given that

Q: Evaluate the integral dx 2VX3 - 3x Vx 1 V3x - V2 +C In 2/2 /2 + V3x In 1 +C 2/2 2 - V3 O In(2 V x3 -…

A:

Q: 2. y = x2-6x +8 Y UR Оpens Vertex_(3,29) Axis of symmetry. x-int. y-int (0,8) domain range

A: Given y=x2-6x+8 ⇒y=x2-6x+9-1⇒y=(x-3)2-1 ⇒y-(-1)=(x-3)2 Which is comparable to y-k=A(x-h)2, where (h,…

Q: 2. Use the fundamental theorem of calculus part 2 to compute the integral 1° dr. 0,

A:

Q: | In(vE + 5)dt

A: Given: I=∫lnt+5dt  ……1

Q: Find of z = In(xy)

A: Given,Z=ln(xy)differentiating both the sides partially w.r.t. x∂z∂x=1xyy1∂z∂x=1xagain differntiating…

Q: ntegral of 1/((1+2x)^2)

A: given integral, ∫1(1+2x)2dxwe have to evaluate the given integral

Q: 5. Integral ReR dR

A:

Q: 7. ydx-xdy + xydy = 0 Ans: In²+ y = c

A: We have to solve differential equations

Q: What do you mean by euler's theorem?

A: Euler’s Theorem is a generalization of Fermat’s little theorem dealing with powers of integers…

Q: Anti der ivent ive 2x %3D 37-4

A: Solution

Q: rV4- a² dx

A: Let's find.

Q: State Fubini’s theorem.

A: Statement of Fubini's theorem

Q: Differentiate y = laz az-1 In r Option 2 None of these 2n In z Option 3 Option 1 2ln-1 In z

A:

Q: . Solve using integrable combinations. ydx + xdy + xy(ydx – xdy) = 0 |

A: Consider the differential equation  ydx+xdy+xyydx−xdy=0........1 We have to solve the given integral…

Q: sketch . reverse then evaluate the inlegration 2X 2 (u x+ 2) dydx X 2

A: We have to evaluate the integral for the given region between y=x2…

Q: Еxercise 13 Determine how тany times 0 арpears in thе тultiplicatioп table for Z16-

A:

Q: Ex: well defined?

A: Yes. It's well defined norm function.

Q: 6) Prove mathematically that (1 grad = 0.9 deg) %3D

A: Since, this is a multiple question according to the Bartleby Answering rule, only first question is…

Q: bounded by + 22 %3D

A: z>0z=x2+y2z=1-x2-y2Intersection;x2+y2=1-x2-y2x2+y2=1-x2-y22x2+2y2=1x2+y2=12x2+y2=(12)2;  circle…

Q: State Green’s Theorem

A:

Q: Explain Fubini’s Theorem.

A: Fubini's Theorem: If f(x, y) is a continuous function on a rectangle R=[a, b]x[c, d] then the double…

Q: +1

A: I have stated the used formula in the solution

Q: 9 In(z² – 1) dz

A: Given: ∫9lnx2-1dx

Q: 23. -(-Cnd)→e -evd dz

A:

Q: Evaluate the integral. 4 sec2(2t) dt 3+2 tan (2t) 2 4 sec (2t) dt%3D 3+ 2 tan (2t)

A: See the details solution in below

Q: 10 de . 4+3cose Integrate

A: To evaluate the given definite integral.

Q: What is the integrable form of dr? du u du

A: Given integral is:

Q: Number 8

A: first find the derivative.

Q: Integral of cos2x on [0, infinity]

A: We have to use limits to find the given integral.

Q: .3 1+ at dt

A:

Q: integrate the fallowin 4 (usın'sx lx

A: Given: The trigonometric identity that can be used to simplify the above expression.

Q: Iterated integrais. 3. ( ye* dx dy Jo Jo

A:

Q: Evaluate the integral. '3 4,3 3,2 dt -

A:

Q: How do you integrate z/(z+2) in terms of z?

A: Here, integral is,

Q: 1 Integrate 1+25cosx

A: To evaluate: ∫11+25cosxdx Let, I=∫11+25cosxdx Since, we know that cosx= 1-tan2x21+tan2x2…

Q: dr 4 – z Integrate:

A: The given integral,∫54-x2dx

Q: find inmporopor integreal STæra o dze

A: To solve the improper integral

Q: nly.

A: Given equation is :  -√3 sin(x) + cos(x)

Q: Integrate: dr z2 + 4z + 8

A: We will integrate the above expression.

Q: 38 Show that x² V2x – 3 dx - 35

A: use the formula below to evaluate the given integral.

Q: Prove that 1- cosh -1 x= In(x+ Vx- -1 1 x+1 2- coth -In x-1 X = - Vi+x? .2 1 3- csch -1 x = In(-+

A:

Q: dt 4e -et

A: To evaluate the integral: ∫dt4e-t-et Solution: Given integral can be written as:…

Q: 10 9. Integrate 4+3cose de.

A: To evaluate the given integral.