5. If x is an integer, then x' 2x. b d a C 6. There exists a real number x such that x'= x . FL

Q: 7. S(1)=3e cosh (In 2r) in two ways.

A:

Q: Solve for r: In(x) + In(x + 2) = 3

A: Use the properties of lograthim and simplify.

Q: 3) Prove that ae*+be-x a) b b > 0 ex+e~x

A:

Q: 14. Consider that * Sof (x)dx = 2 and f'(1) = 3. Find Soxf"(x)dx. %3D 3 O 5 O 1 O 4 O 2

A: We have to find

Q: Compute for the value of tanh (1 – i) Iny + 2.13i In 2 + 2.13i 2 In 5 - 4.25i 2 In v2 + 2.13i

A: To Compute: tanh-11-i Concept: 1. tanh-1z=12ln1+z-ln1-z2. lnz=lnr+iθ+2nπwhere,…

Q: 6. Show that, for integer s, S. s! | x25+lexp(-ax²)dx =: 2a +1

A: Note: Given proof statement has a little mistake, I have proof the actual result. First i have…

Q: Express In V16 in terms of In 2 and/or In In 16 =[ (Type an exact answer.)

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: now tha 4.31) and that cov(y-ΣΣ) Σ- as in 4.32). – E,. x) = ΣΣΣ as in (4.32). %3D

A: E(y-∑yx∑xxx) = E(y)-∑yx∑xxE(x) = μy-∑yx∑xx μx AS E(y) = μy E(x)=μx ∑yx is the covariance marix…

Q: 2. f(x) = In 3r on [1,4 with n =5

A:

Q: 1 Show that 2-* d.x 2 In 2

A: We can show the answer in the following steps.

Q: : 2 < x < 4} and B = {x € R : –4 < x < 1}. Prove

A:

Q: A. Homo ge neous Higher Ordered DE (0-704 - 310° ° + 103o² 1030² + 1500 - 216) y:0

A:

Q: 22. Differentiate the following with respect to the variable x, giving your answer in a implified…

A:

Q: 2.If alb and alc then al Cbx tcy) for all X>YEZ.

A:

Q: 4. ( Give a case in which |(x, y) |xlly|l.

A:

Q: 2. TER-1 to be, Hn E IN 1+r+4---+ 1-r Shoh that

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Q.2) Evaluate cln 7 cln 2 cln 5 e(z+y+3) dzdydr In 6 In 4

A: Given triple integral is ∫ln6 ln7∫0ln2∫ln4ln5 ex+y+z dz dy dx   Note:- ex+y+z =ex ey ez

Q: 2) Show that (1 – x²)P",(x)P'm(x) dx: 21(l + 1) Sim• 21 + 1

A: Given:-  ∫-11(1-x2) p'l(x)p'm(x)dx=2l(l+1)2l+1δlm

Q: 4. If x = cose + isin0 & 1 + V1– a² = na then prove that 1+ acose =(1+ nx)(1+) %3D 2n

A: Given, x= cos θ+i sinθ and na=1+1-a2      To prove:  1+a cosθ=a2n(1+nx)(1+nx)       Let  x=…

Q: 11. Evaluate the integral. +3 x² + 4

A:

Q: Find dy ax 9=бл+бай

A: Given :y=x+1+xformula : ddxx=12x

Q: 12. If IN = 2x + 10 and AT = 26, find x. %3D %3D В 丰 N A O 6 O 12 О 10 8. -

A:

Q: If Pn: 49^n +16^n + k is divisible by 64 for all natural numbers is true, then the least negative…

A:

Q: -2 -In x SLy e dz dx dy O 7/24 O 7/48 O 5/48 O 47/24

A: We have to find the integral.

Q: We now need to attempt to find an exact value for n such that P(r ≥ 1) = 0.99. Clearly, if the…

A: We have to fill blank of P(r ≥ 1) = 1 − P ( ___ )

Q: 1. Differentiate the following with respect to x: a. y= 5x - + 5Vx + 3p ex + In(x) - 7 (9)

A:

Q: Suppose we observe X1, X2, ..., X U (0, 1). Show that nX(1) 4 Exp(1). с.

A:

Q: 13. - (In t ² )º t dt

A:

Q: 6. Show that =+ E-(-1)"(n+ 1) E)". when Iz – 2| < 2.

A: Seriese expansion

Q: 42. Show that S 4xys + %3D 1- x2 1- y? 1– 22 (1 – a²) (1 – 3²) (1 – 2²) if xy + xx yz = 1

A: Given that  xy+yz+xx=1 Prove that the expression

Q: 11. Prove that tanh y du = In cosh u + C

A: The integration of the integral is tanhu.

Q: It is possible to regress x1 on y. a. True b. Falas

A: From the given dataset we have to check that , is it possible to regress X1 on Y1  or not.

Q: Suppose X~N(148,8), and Z~N(0,1). Then x = 143, is equivalent to z = ______. (Round your answer to 2…

A: Given information  X ~N(148,8) Population Mean (µ) = 148 Standard Deviation(σ) = 8 X= 143

Q: FOR N=195, by fermat's theorem an-2 =

A: Given: FOR N=195, by Fermat's theorem an-2

Q: 3 If [E dx = In(7x - 6) - +C, find f (1). 7x - 6 Enter an integer or a fully reduced fraction such…

A: Given that:-∫f(x)xdx = ln(7x-6)-37x-6+CTo find: value of f(1)

Q: 2 In x | Show that 4 x* +1 16

A:

Q: Suppose X~N(112,16), and Z~N(0,1). Then x = 112, is equivalent to z = ______.

A:

Q: 4. Show that In sin 6 d0 = – n 2 by applying the mean-value principle to In |1+ z| for |2| <r < 1,…

A: ∫0π2logsin(θ)dθ=12∫0πlogsinθdθ                         =12∫0π2logsin2θdθ…

Q: 5 Evaluate ſ“ S" r² sin ø drdøde 0,

A: Evaluate: ∫02π∫0π∫05r2sinϕdrdϕdθ

Q: 4. Show that if ki = (X; - X)/[Σ(X; – X)2], then (a) Σki = 0; = (b) Σk? = 1/[Σ(X; − x)2]; (c) Σκ;(X;…

A:

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

A: We know, that 1grad= 0.9 deg.  we can solve any other similar problem by multiply the number of…

Q: 8 Show that 1+2++ In S 1|+ |r2|++|rn| for any numbers r1, 22, ....

A: To show,    x1+x2+.....+xn≤x1+x2+.....xn   for any numbers  x1, x2,....., xn . Which is generalized…

Q: 6. Given that -뿔 (금) (규 R(x) 4! 1+. for x E (-, 3), where & is between x and 0, find an upper bound…

A:

Q: Compute for the value of tanh-(1 – i) In 5 my + 2.13i In /2 + 2.13i Inv - 4.25i 2 In /2 + 2.13i

A: Let, tanh-11-i=z. Thus, solve for z:…

Q: 26. If z = In(x² +y²), find x- ду Əx A) х с) у в) х-у D) 0

A: If z=ln(x2+y2), We need to find x∂z∂y-y∂z∂x.

Q: Suppose / (s) - (÷)*" valuate: Js(x) dr +C 3- In (5)

A: Given      f(x) = 1512-3x

Q: #02:-Discuss all the cases of reducible to hamggenou D.E form.

A:

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.