Q2 Which of the following is equal to 54 +V4? (A) V128 (B) V56 (C) 216 (D) VI12

Q: Q: Find the middle term af the fo llowing (5x-1y)5 10 シャ 2.

A: 2x+x210 use binomial theorem a+bn=∑i=0nnian-ibi 2x+x210=∑i=01010i2x10-ix2i to find the middle term…

Q: What is the order of y"(t) + 9y(t) = 10?

A:

Q: Q3: if it was V2 B =1.A = [VZ o 3] 1.A [V2 O 3) Find В.А A.B , VZB

A: 3B=21-2 ,  A=203B.A=21-23*1 , A= 2031*3=222023121013-22-20-23=2032203-220-6

Q: Q4. Arg (--) = + 2kn 7n + 2kп 2n 5n .풍 a. с. d. 3 6

A:

Q: If || v || = 2, what is || - 4v || ?

A: From the given data:

Q: Q5 1 Find proj; (w) where w= and v = 2 -2 3

A: Solution:Given     w=10-2     and     v=123To find:projvwFormula:projvw=P wwhere P=v vTvT v

Q: (b): Evaluate: (8t³ – 9t² + 10)dt

A:

Q: u = ? - 5r – 21 +3, v=r - 4² – 31+4, w= 2r – 17? – 71+9.

A:

Q: (c) Try two ways: using the 1) quotient rule and 2) power rule. dt

A:

Q: What is the GCF of the expressions 115rs^5(2r+s)^3 and 100r^3s^4(2r+s)^7?

A: To find the GCF of the expression: 115rs5(2r+s)3 and 100r3s4(2r+s)7 Simply write the complete…

Q: 7 k(x) = 2r2 - 3Vã, then k(9) is 1) 159 2) 153 3) 315 4) 307

A: given function as k(x) = 2 X2 - 3 x  k(9) = ?

Q: Q.2) Evaluate r8-z² 4 dzdydx 0.

A:

Q: (a) For what value of n does V· (r2nêr) = 0? (b) For what value of n does V x (r2nêr) = 0? %3D

A:

Q: Find a counterexample in the following cases. 5. (P^Q⇒R)⇒(P⇒R)^(Q⇒R)

A: As per our guidelines,we are supposed to solve only first question. Kindly repost other question as…

Q: V16-x² B Evaluate S. Sezy2) (x²+y²) /16 –r²drdzde -

A: Given integral is, I=∫04∫016-x2∫x2+y24416-r2drdzdθ Now, integrating the given integral,…

Q: 78- 6y 17s

A: When the four vertices of a quadrilateral lie on a circle then the quadrilateral is called a Cyclic…

Q: o the emergency room of a small hospital is 2 it, on any giv wły admitted patients?

A:

Q: Find m21 and mZ2. Justify your answer. 52 m21=° by the

A:

Q: 10. JK 7t + 15 10t K

A:

Q: Now gx y"_y₁-2y=C₁e +4c₂e² २०७ +4₁e - alge 20₁0 x 2c2e

A:

Q: Find L[6t³ + 11e¬24] 11 s+2 11 -2 을 + 플 꽁 + 플

A:

Q: Which of the following is equivalent to 3 - V2 O A. V2 А. O B.-V2 3- V2 O C. 3+ v2 O D.

A:

Q: 3 What is the value of V225?

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: ZA is supplementary to ZB and ZB is complementary to ZC. If mZB = (12x + 8)" and mC = (8x - 8)",…

A: Complementary angles: Two angles are complementary if their sum is 90o. Supplementary angles: Two…

Q: d. Evaluate dr ((5x² + 10)e) at r = 2.

A: We will differentiate the given expression using the product rule and then put X equal to 2

Q: 1. Simplify: d) v V45x45 e) Vm13n23 m13 f) n23

A:

Q: Q3 Suppose that X ~ N(-8, 14). Find:

A: Consider X as a random variable that follows a normal distribution with mean (-8) and standard…

Q: Q8 Find the Fouter trarsfoms ot : pn sx<pm otherwise Take p -9

A: Fourier transform

Q: Q2) Find the avea of the Vegions enclused by X = 2y X = o and 9 = 3

A: First we will sketch given curves and identify the region enclosed. Using the sketch and…

Q: Q2) A Differentiate the following ( 1)y= [(5x) (4- 2x)]²

A: As per bartleby guidelines we only give first question answers.

Q: Q2) By using the Lagrange interpolation method, estimate the value of y(0.5) where y(3) = 0.62 ,…

A: Lagrange's Interpolation formula is, f(x)= (x-x0) (x1-x0)×y1+ (x-x1) (x0-x1)   ×y0f(x)= (x-x0)…

Q: Q4. Given that 30-3 1 0 1

A: the given matrix is A=-10130-310-1 The characteristic equation is A-λI=0…

Q: Q2 Find Domiain and Rang メー2 2. y = 3-X

A: Given y = x - 23 - x

Q: Evaluate the following: d)13P4 e)11C6

A:

Q: find w3, of 8+ 8/3i O2/15° O2/285° O2/105° O2/195°

A: The given problem is to evaluate and simplify the given complex expression and find the value of w3.

Q: 8. 2z (z – 1)?

A:

Q: FIND THE RE MX | |H6 pxpts oF THE SpHtMCAL TMANCLES 3) C- 90° A = 19045 '37" , B - 87°33' 18" リ

A: Given,C=90° , A=19°45'37'', B=87°33'18"To find: Reamining parts of spherical traingle.

Q: 3 V= ㅠ (x4 – 18x? + 81) dæ 3 18x? = T + 81x n 5 3 [(-0)-(뿌 ) -0) + 18.3 3

A:

Q: Q3/ Evaluate grad d, If In(x+y+2).

A: GIVEN: ϕ = ln x2 + y2 + z2

Q: 3y(y+7) Simplify (y+7)(v² – 9), under what conditions is this expression undefined?

A: Given a fraction : 3y(y+7)(y+7)(y2-9) We have to simplify it and also determine under what…

Q: Szdx is 2(1 – x²)7 +c is it: +c_ is it : V1-x a)True b)false

A: Use sin²x+cos²x=1  And integrating the function  We get the required result

Q: Q2 || Find Def , where ((x) = (x) =

A: The functions are f(x)=1x-1  &amp; g(x)=xx-1 The composite function of f(x) and g(x) is defined as…

Q: A student did this: /5 +V7 = V35. His answer is incorrect. Describe his

A: 5+7=35

Q: -48 36x y 6. 12y' ³ 53 - 4 pq°r 8. 8p q*r 2 210

A:

Q: x3+1. (xZ +4)? Parhal frachon 8. 2

A:

Q: Q4: Answer two only: 2 1 -1 (A): I A=2 -2 Find AB and AC : - 1²/2 3 11 -2 -2 and 2 -- }

A:

Q: 7R1 + R2 → R2 А ТА ----

A:

Q: Is there a difference between "52and 1 !522? Explain

A: We know that x2=xx2=x2 Similarly, 52=5=±552=5

Q: y = 0.005 e und the prob that a dife now aped 30zat wulu die between the agu 65 965.both verack.

A: 1] μx=0.005e0.09x-20 2] exact life aged is 30

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.