If the statement is true, prove. If the statement is false, disprove. 1 + 2" > 3n for all n E Z

Q: Produce a simple formula for a where a, n € Z and 1 ≤ a ≤ n. i=a

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Q: 1. Find the value(s) of x that satisfy x? – 3.5x + 1.8 = 0.

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Q: Show that if x > 9, then x³ – 8x? + 2x > 3. Show that for all n e N, if n > 10, then nª – 2n² > 3n³.

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Q: 2. In the figure, 21 = 2, 23 = L 4 and BD = CF. Prove that AC = EF and AB = DE. E В F D C 2.

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Q: If k> 0 such that O St the above 4* dx = 3 then k = 2ln 2

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Q: The sum of the first p,q.r tems of an A.P. are a,b,c respectively. b Show that (4 -r)+…

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Q: Given the DE as 2xy² + 4 = 2(3-x²y)y'. A. prove or disprove if the given D.E. is exact. B. If it is…

A: The given differential equation 2xy2+4=23-x2yy' Exact differential equation:    The differential…

Q: What is the value of k if any So kxe* dx = 1

A: This question is taken from the Definite integral in which we have to find the k value by solving…

Q: e 1 for sub

A: Solution of the problem as follows

Q: O Solve the eguation, Kdz x dz - gdz +ze (tya) Ans OF THS + -z) =0

A: This is linear equation so we can use Lagrange auxiliary equation to solve this problem.

Q: (b). Find the value of z if e =1.

A: Solution: Consider the equation : ez = 1 Now, taking natural logarithm on both sides we have ln ez =…

Q: Find a number a + 5 such that S" (1 – æ) dæ = 0

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Q: s evaluate e of 1. The

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Q: :""n e Z*, if n³ = 3k for some k E Z, then n = 3q for some q E Z." %| %3D

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Q: Solve the following formula for the specified variable. P = 3rz for z (Type an exact answer, using a…

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Q: Find n if P(n+14,2) = 756. Show your steps using the formula for P(n,r). LIca tho aditor to fo

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Q: (a) Find all the solutions of e²+e¬z cosh z 4. (Hint: cosh z -) 2

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Q: Find z-transtorm For (n-1) X(n) (a .1) u(n-1)

A: As per our company guidelines, we can solve first question for you. If you want other question to be…

Q: Let p and q be integers with q>0. If y= x^p/q, differentiate the equivalent equation y^p=x^p…

A: Condsider p and q are the integres. We have to check the formula ddxxpq=pq·xpq-1 is true or not if…

Q: (2) Assume X(@) 0 for all o e Q then which of the following is not true: (a)4-r X+X ±1 (b) XX = 0…

A: The must be option c

Q: Prove L{a coskt}= -at S+a

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Q: Given the explicit formula, find the first 5 terms. f(n) = 3"-1 %3D

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Q: For any positive interger n, (n + 1)! / n! - n = (A) 0 (B) 1 (C) n (D) n + 1 (E) n!

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Q: For all n, d EZ where d + 0, d\n n = dk for some kEZ. Disprove: For all integers a, 6, and c, if…

A: I have disproved the result

Q: Excercise 1. For small e, find the first two terms in the expansion of each of the roots of P(z,e) =…

A: The given polynomial: For small , Take Substitute value in the given polynomial, This can be…

Q: fferential Eugh by finding tor. (6n +only)dy=0)

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Q: Solve e = 1 + V3i for all values of z

A: Given,              ez=1+3i

Q: Using only a simple calculator, find the values of k such that det(M) = 0, where 4 k M 1 k As your…

A: M=-4K011K11-8detM=-4-8-K-K-8-K          =32+4K+8K+K2          =K2+4K+8K+32          =K+4K+8

Q: g) Finally, we can manipulate the above formula to solve for î. Show that k = (AT A)-'A™b.

A: Given information :  ATA is invertible.

Q: * The evaluation of So So x y ex² dxdy is 0.25 e - 0.5 0.25 e - 0.25 None of them

A: The objective is to evaluate the double integral.

Q: Which of these is a possible solution for cscx + Oin the interval 0 < x < 2r? O x = 3 O x = 3

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Q: The following series 3 2n+1] (-1)" 4n 3n n=1

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Q: For any natural number m, evaluate 1/m +x")( 3m 2m 2m +x 2x +3x" +6)"* dx, x > 0. m X

A: Topic:- Integration

Q: 5n2 For E>0, there is a corresponding N such that -4/0 N. 4 +3 Then the value of L will be

A: Given function is , f(n)=5n24n+3

Q: Given S CRis closed and x > 0 for all x E S. Prove inf(S) is positive (Hint: In this case, inf(S) +…

A: Given S is closed subset of R with x&gt;0 for all x belongs to S. To show inf(S)&gt;0 We know-  Any…

Q: 3. If f (t) =Vt, g (t) =, and h (t) =2t-4, find the formula for f (g (h(t))).

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Q: 1 x? + k by considering several cases for the constant k.

A: Let k be equal to a2. k=a2a=k Use the formula ∫1a2+x2=1atan-1xa ∫1a2+x2=1atan-1xa∫1k+x2=1ktan-1xk

Q: Q2) n(x) = x-1 , k(x) = (x – 1)/2, mx) = (x + 8)¯1 (x + 8)-1 Find a formula for ( m onok).

A: See answer below.

Q: ssume that an = for all n E N. If lls us that: a) SE (0.6,0.7] b) SE (0.7,0.8] c) Se [0.8,0.9]

A: In this question, the concept of the sum of infinite series is applied. Infinite Series A series is…

Q: Using only a simple calculator, find the values of k such that det(M)=0 where M=[10 k 0 1 1 k 1 1 1]…

A: Determinant: The Determinant is a scalar value that is a function of the entries of a square matrix.…

Q: The Maclaurin sertes for 1(x) -eli) (e) (b) (e) Nome kt (e)

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Q: AE and DE intersect at E. 2. Given: AE Prove: * BE = = DE CE

A: Given, AE and DE intersect at E.

Q: The set of values of K such that dx is an improper tnte gral is 2x +K a) - 14 <K <-4 b) - 14 < K <…

A: Improper integral - An improper integral is a definite integral that has either or both limits,…

Q: Solve e = 1+ V3i for all values of z

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Q: Prove that the value of the expression (а — 1)(а — 3)(а — 4)(а — 6) + 10 is positive for every a E…

A: The critical points for the function are the set of values where the function attains its maximum…

Q: The characteristic of Zs[x]/ is 6. 3 O None of the choices

A: The characteristics of the function

Q: Find the largest number ổ such that if |x – 2| < 6, then |2x – 4| < 6, where e = 0.5. Repeat and…

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Q: Find all values of t for which det(t I3 − A) = 0 for the following:

A: A=  2-2  0-3  1  0  0  0  3 Now, t·I3-A=t100010001-  2-2  0-3  1  0  0  0  3=t000t000t-  2-2  0-3  1…

Q: 27 Find (all) the value(s) of c such that 3cn %3D - 8. n=0 (A) c= 3 (B) c= 4 (C) c = (D) e (E) e (F)…

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Q: 2. Which of the following tvas is a model for the following formula P+ (-(Q ^ R) V S) Р: T Q: T (A)…

A: We have to choose the correct option which satisfies the condition of the following: P↔¬Q∧R∨S. First…

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.