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Q: sn'x プェ Sec'x-1 from [o, of 2.

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Q: Q3: Prove that Σ(y₁ - y) = 0 AND Σfi(y₁ - y) = 0

A: The question is about proving given equation. To prove : ∑ ( yi - y¯ ) = 0∑ fi ( yi - y¯ ) = 0

Q: Q4/ if f(x.y)=x-y and g(x.y)=3y prove V2) gVf-fVg g? %3D

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Q: Using the Convolution Theorem, what is L[h(t)]?

A: In this question, we use the convolution theorem to find the Laplace transform of the given function…

Q: eralvate s Ēodp where C is represientee ぐ F (Xっy)= yi 土 6+) = 28ti + tj

A: To evaluate: ∫CF.dr→F→x,y=xyi^+yj^rt=28ti^+tj^ ,     0≤t≤7

Q: X,X, X3 R.S. T3 %3D Bind dis tribution of Xo

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Q: J x(1-Sx2)4 dx

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Q: f the function. [(x, y) = x²y³ + x, t) = √√√x In r =tan xy (x, y) = x² = e²/(u + 11²)

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Q: 03. Find se and *. If f(x,y) = 2e* + Iny² ,and x = 2t + r2, y = ; %3D at r+1

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Q: 1 Using Convolution theorem, find (i) L (s+a)(s+b),

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Q: Let (1-t)y +ty -y= (t² – 1)e*. %3D

A: Reducing it into standard form, we get, y''+t1-ty'-y1-t=-t2-11-tet⇒y''+t1-ty'-y1-t=-1+tetHere…

Q: y z = x + show that : 0.

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

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Q: Q3 Evaluate fII, xyz dxdydz, 3 < x < -2,0 < y < 1,0 < z S.

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Q: Use the Runge-Kutta 4th order method to find the values of y where x is given that y = 1 when x = 0…

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Q: dy Find Z for y = (8+ x³ In x)ª + e3x

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Q: Let f(t,y) = y+ 3t?e'. Then f satisfies a Lipschitz condition in y with L = 2, given that 1sts2.…

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

Q: At time t hours a company is selling items at a rate of r(1) items per hour. 10 Interpret the…

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Q: 2016 J Q2 () Express 4x + &r-5 in the form p(x+q) +r, where p, q and r are constants to be

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Q: dx Show that f - In|ax + b| + C where a # 0. ax+b

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Q: Detemine the x-values at whìch, 9水)= 2xー 3xー+X メt,xE - スxナラメー3x underined. Evaluate the linit ac…

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Q: The evaluation of S V1 + tan2x dx is C In(V2) +1 In(vZ+1) C In(vZ-1) O-In(vZ+1)

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Q: af axdy of f (x, y) = xy(x+y — 1) — x² Find-

A: The given function is: fx,y=xyx+y-1+x2   As we know that; The Power Law: ddxxn=nxn-1 The Product…

Q: Calculate the LOS of y = x² LOS is x = a is b is c is

A: Given equation is in the form of ax^2+bx+c=y Here a=1 b=0 C=0.

Q: Oo Find a functiom f and a nunber a E(4,7) such that I+/" f(t) dt = tan x a number a c(#,) Cost

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Q: Find PSD of Y (i) interms of X (1). Assume O is independent of X (f).

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Q: Making use of the fact that ˆα = y − βˆx and βˆ = SxySxx, show thatni=1[yi − (αˆ + βˆxi)] 2 = Syy −…

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Q: Find. all.Second.parkia.devevatives:.. a. fcx,y.).n(3 x+5y)...b,uze sint C.Z=ytan2x

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Q: Let T = x²y-xy³ +2; x=rcos0, y=rsin 0. Find and OT at or 20 TAT

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Q: Q2) Is the ODE separable or non dy x² + 3y2 2ху

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Q: d²y Given that x3 + y³ = 2, prove that 4x dx² y5

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Q: (3) = 2 u + U, =D2 at ucx, t) fipdy ing the following initial condition : - -3X U(x,0) = 6e

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Q: (2 fi = f(x²+xyz, y² +22= Prove that (y²-2x) ou 2ZX) then ne (²h-x) he 18

A: Concept: Partial derivative : The partial derivative is similar to the normal derivative except in…

Q: Gy Let Px) = x²/3, x. thens Rx) = x2/3 ×シ。 then: %3D O Find ê cx) ? 2 Gruphs off R and f

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Q: Q8) Find the Linearization f(x.y.z) = x² + xy + yz +? at (1,1,2)

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Q: Q: If u =f(x² +2yz, y² + 2=x)Prove that (y-ax

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Q: H.W. a PDE from the followi'ng- @u=f() Form メツ 0u=fcx?ー)

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Q: Q3/ prove fry = fyx if f(x,y) = x + xy – 5x³ + In(x2 + 1)

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Q: 2. Derive a formula to approximate S* s* f(x;y)dxdy yo xo Using Simpson's rule with x2 – xo = 2h ,…

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Q: af Find and ax af Jy f(x,y) = e⁹xy In (3y) 11 for the following function.

A: To find the partial derivative.

Q: Q3: Find the value of n which F(x, y, z) = (x +y +z*)" to satisfy fxx +fyy+ fz= 0. 1

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Q: b) u(х, у) on the domain 0 < [z| < ∞. x² + y? Why is v(x, y) single-valued in b?

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Q: af when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y ,x = 2t + s, y = 2s – t. a) Find as

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Q: f(z) =z? is discontinuous

A: f(z)= z2 is a polynomial function in z and polynomials are continuous everywhere.

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.