Let a be a constant. Given that *(24-) 62 find In a 3 3z In(ar)dr = e %3D

Q: 10 X =1.2 is to be sol he initial approxima

A:

Q: a=t). CTaylon Serie) 2-X Ln +x) (MacLurinSeries

A: We need to find the Taylor series of f(x)=12-x at a=1. Taylor series of function fx at a is defined…

Q: The Weber-Fechner law states that if Y is the physical intensity of sound and X is the perceived…

A: From the given information, fY(y)=ye-y22, y>0 And X=klog(Y)Xk=logYeXk=Yexk*1k=dydx

Q: 1. Let X1,..., X, be independent, X; ~ exp(A;). a. Show that Y min(X1,..., Xn) is also exponential…

A: The exponential distribution is a continuous type distribution. The density function is defined as…

Q: 1. Let X1,..., X, be independent, X; ~ exp(A;). a. Show that Y = min(X1,..., Xn) is also exponential…

A:

Q: A 15-gram sample of radioactive iodine decays in such a an that the mass remaining after t days is…

A:

Q: Let xn ≥ 0 for all n ∈ N. (a) If (xn) → 0, show that (√xn) → 0. (b) If (xn) → x, show that (√xn)…

A:

Q: (In (ev) + e-V): d Let a be a real valued constant. Then True False

A:

Q: 73. Use the definition of |x\, the chain rule, and the fact that (In x) = - for x > 0 to prove that…

A: Given, dlnxdx=1x, x>0 from definition of x x=x ,     x>0 -x ,  x<0  if x>0 then d…

Q: sion By A knawn x²-5x_x+5 ーちメメ -X cr ar

A:

Q: What is the largest positive constant K such that if 0 O A. e O B. 1 O C. e1 O D. e?

A:

Q: What can you say about the upper bound of E(x) for numbers of the form 3^(2n) + 1?

A:

Q: Find g'(3). g(x) = In(1+t) dt In(4) 6ln(10) O In(10) 3

A:

Q: IF X has an exponential distribution with the parameter 0 an Hy = 202, where 0 >0 then find µx, a,…

A: Given that X has exponential distribution with parameter θ. μx=2σx21θ=2*1θ2θ=2 Therefore,…

Q: Evaluate: dx. x-2 A) In 3 - In(-2). B) The integral diverges. C) In 3 - In 2. D) - In 3 + In 2. In 3…

A:

Q: Let a be a constant. Given that 3z° In(ax)dr = e® ( 10 – - -23 find In a. 3

A:

Q: Find a general formula for dr ax + b dx" cx +d

A:

Q: Use mathematical induction to prove that the n-th derivative of (x +n + 1)e" is given by d" (x+1)e =…

A: We use mathematical induction. The detailed solution is typesetted and given in detailed as the next…

Q: Find the value of k that makes the antidifferentiation formula true. |(1- 10x) 1 dx=k In |1– 10x| +…

A: According to question given that ∫1-10x-1 dx=k ln1-10x+C

Q: Prove that coshz =log ztv= {Hint : cosh z =e} 2.

A: Use the hint and prove this.

Q: f substance B, in milligrams, left after t years, given that the initial quar

A: Option of part c is A.

Q: A- Find the integrating factor of the following D.E 2

A: a) Here we have to find the integrating factor of given differential equation:-  We have,  Compare…

Q: 3. Derive the reductive formula for S sec" (x) dx.

A: We will find out the required solution.

Q: Let a be a constant. Given that ) -71 3z In(az)dz = e2 ( 28 - find In a.

A: It is given that the integration ∫1e43x2lnaxdx. Use integration by parts to simplify further. Let…

Q: If P(x) = -1/x then the integrating factor is a. e-* 1 b. С. -x d. e-1/x

A: Consider the linear differential equation: dydx+pxy=qx The integrating factor for above linear…

Q: 1. Let X1,..., Xn be independent, X; ~ exp(A¡). a. Show that Y = min(X1,..., Xn) is also exponential…

A:

Q: Let X ~ T(a, B). If E(X) = aß and E(X²) = aß² + a² ß². If â = X, find the method of B moments…

A:

Q: Let a be a constant. Given that 3x² In(ax)dx = e° ( 18 3 -44 + 3 find In a.

A:

Q: Let X - x? (s). Find (a) E (1+2X + X²) where E (g (x)) = 6° g (x) fx (x) dx. (b) the characteristic…

A:

Q: 1. Let X be a lifetime (in hours) of a lightbulb and suppose that X has a PDF of (e0.001x f(x) = {…

A:

Q: Let I be ar. V. has a Binomial dist. B(n,@) with the Pid.f. fex; G)o-0^,X:o,n Show that fex;)…

A: Given that X is a random variable which has binomial distribution Bn,θ with p.d.f is given by:…

Q: 6. 81n V81 - 81 – x²dx 4 A. Show that B. Use (A) to evaluate In 4 (e2x – e*) /81 – (e* – 1)* dx. - -

A:

Q: solve for x if CDy=4(x-E)

A:

Q: Show that -E{t, log(sigma(w*x)) + (1 – t;) log(1 – sigma(w"x;))} = E, log(1+ e-yw* x %3D Where…

A:

Q: Let a be a constant. Given that e6 -107 | 32° In(ax)da = el8 ( 42 – find In a. 3 3

A:

Q: Calculate the residue of e.e5=0

A:

Q: Find if y = [In(e* + 1) + ešin #]³. Do not simplify.

A:

Q: If X and Y are independent and identically distributed exponential variables with parameter X = 4,…

A: We have given : X & Y = independent and identically distributed exponential variables Parameter…

Q: 39. Find two numbers a and b with a < b such that [(6 - x - x) dx has its largest value.

A:

Q: Specify c_1, co, C and p such that the formula c_1u(8 - h) + cou(s) + cu(s+h) hP u (s) 2 denotes the…

A:

Q: Evaluate. e14x (e14z +13)² (Note that the constant of integration is already included) dx +C

A:

Q: a) the linear approxinma ion to the function + 3X ät

A:

Q: Find P(2 0

A:

Q: dx Evaluate the integral: 3/2 64 -

A: To solve the given integral problem.

Q: Employ Stirling's formula to compute y122 from the following table Vx =1 + log10 sin x): 10 11 12 13…

A:

Q: 5. Show that |Logz|<|In(z)|+ t, for all z # 0.

A:

Q: Given  n constants  ki (with i = 1,2,...., n) and n functions fi (x), deduce from Rules IV and V…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.