Let a e R" and let A = aaT. Show that xT Ax = (a" x)².

Q: Q2/ Prove that 1 dx = v2 Jo 1+sin(x)

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Q: du ap B) Prove that dx n- dx v2 where u = f(x) and v = f(x).

A: To find  d(u/v) /dx

Q: f"Ve-1) de (e* a) (e ) da Ante 1) de Bos birak

A: The volume of the solid formed by revolving the region bounded by the curve y=f(x) and the x−axis…

Q: 2. given that y = 0 at r=1

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Q: Find 1-a Conf int for y txo P( - tor;ou L T L tarziv) =1-a

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Q: If t = x + ex, find d2x/dt2 given dx/dt = 1 / 1+ex.

A: dcdt=0 , where , 'c' is any constant. dexdt=ex .dxdt

Q: ex: show that (H.W) (xJ,(x)' = -x Jv+1

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Q: Show that Ě = 3xyê+G)+2Ê is R3 and Pind Conservative a potential Ø Rar F. on

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Q: ue of the det e 16 is

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Q: Use two different methods to calculate dzu/ar if u = /x² + y². = est, and y = 1 + s² cosz. IUse two…

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Q: Let Xn ☆ Bil^,p] where n& P ae wnknown. Find method of moments estimators for n&

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

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Q: if x²+y²=t-- and x*+y*=t*+=,prove dy X t dx 3. ху

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Q: In SRSWOR show that E(y )= Y

A: ANSWER: For the given data,

Q: a Ex Let mxy+2), x=Git, yosint Find dw at t:3.

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Q: 11. If F(z) = | V1+4t² dt, find F'(x) sin z

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Q: az Find for z = x'y'eV

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Q: If F (x) = (t2) dt , then F' (4) = cos 0,

A: DUIS rule is used

Q: Use at least two methods to prove that dr/dt=0 when r=√x2 + y2, x=α cos t, and y=α sin t if α is a…

A: First method   r=x2+y2r=(α cost)2+α sint2            since x=α cost and y=α sint  =α2cos2t+α2sin2t…

Q: Show that d/dz(z^2 z ̅) does not exist anywhere.

A: Here we show that ddzz2z does not exist anywhere.

Q: 2) Show that La- (1 – x²)P',(x)P'm(x) dx : 21(1 + 1) Sim. 21 +1

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Q: Find dy/dr by differentiating implicitly if z +ry- 6r = 2.

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Q: 3. If z = f (x, y), where x = e“ – e® and y = e® – e", show that UTM UTM az az UTM X : az - ду dx…

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Q: Let f(x, y) = 6e sin(7y) af af dy

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Q: Differentiate the following with respect to x: b) 3*Inx

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Q: Let f(x, y) = 7e2" sin(5y) af af dy

A: We can make it easier for you

Q: If z =e* + In(xy) Evaluate- ,and ,at the point (1, 2). Hence, calculate the change in z when x…

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Q: If g(x) = - - S^*[e'- In(2t+1)]dt, find g'(x) . dx A ex-In(2x+1) 4 B

A: We can solve this as follows:

Q: Let f(x, y) = 3e" sin(5y) af af dy

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Q: dz Find if yz – In z = x + y ax

A: To find the partial derivative of z of yz-ln z=x+y with respect x, differentiate yz-ln z=x+y, while…

Q: Compute sec? z + x) dr

A: Given : ∫12sec2x + xdx

Q: If In(ax)dx = 4, then a ( In(ax)dx %3D 1 4

A: we have to find the value of a

Q: Show for Re(z) > 1 -dx = r(z) (2). et - 1

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Q: dy sin(x + y) dx

A: Given , dydx=sin(x+y) Substituting u=x + y dudx=1+dydx Substituting dydx=sin(x+y) in dudx=1+dydx…

Q: Determine the of : In (xy²) = x y dx

A: Derivative dydx of equation  lnxy2=xy

Q: Find y' if exy = e 4x -esy-

A: NOTE: Refresh your page if you can't see any equations. .

Q: if p> 1, (diverges; if p <1. 0o dx Prove that f p- 1 хР 1 Hence evaluate: dx. x6

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Q: dy (a) Find if y = (In x)=². dx

A: For (a), dydx=lnxx2'       =ex2lnlnx'        =ex2lnlnxx2lnlnx'        =ex2lnlnx2xlnlnx+xlnx…

Q: d 1 Prove that: dz (tan¬1 z) = 1+z?

A: Given query is to find the derivative of the expression.

Q: 12- show that x² J.(x)dx = x²J1(x) + x J,(x) – lo(x)dx

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Q: Does the fundamental theorem of calculus imply that e' dt = e*?

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Q: 4. Prove that ах x" ea" dx xn- п-1 ‚ax dx а а

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Q: If u(x, y) = 2 tan-1 2 and v= In (x² + y?) , prove that: a2v = 0 дхду dx2

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Q: (1) So“ dx let t=x o Vx

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Q: Give a physical interpretation of JT. F.ndS.

A: This expression is of surface integral for calculating the area of the field bounded in the…

Q: ven the SRF:Y- BHPXAU Prove that B, Rind B2 estimalors of true fi and Bz are unbiased

A: We need to prove that the  β^0,β1^    are the unbiased estimators of    β0 and β1 In population…

Q: Evaluate 2.xyz dx + x²zdy +x²ydz over the path r(t) = (t², sin(nt/4), e'“-2') for 0 <t<2.

A: The given integral is: I=∫C 2xyz dx+x2z dy+x2y dzOver the path:  r(t)=t2,  sinπt4,  et2-2t    for…