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Q: Directions: Solve the following by getting their derivatives. 4x3-2 1. f(x) x2-5x+1 2. (InVx) 3. у %...

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Q: 2. Evaluate / Fx F - fîdo, Σ where F = (y – 2)i – (x+z)j+(x+y)k, E is the portion of z = 9-x2 – y? w...

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Q: Find a non-linear trend equation from the following three normal equations obtained from the origin ...

A: To fit a quadratic curve y=a+bx+cx2, apply the method of least squares. Use the following normal equ...

Q: In(3x+5e") QIFind lim, In(7x+3e2x) O 0.4 O 0.5

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Q: Ql find chromatic number of

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Q: b. (10M) Find all asymptotes of the function x2 - x+ 1 y = - x- 1

A: We will use the basic knowledge of the theory of asymptotes to answer this simple question.

Q: For what value of 'x', the expression x2 - 7x + 10, is negative? A) 2 > x > 5 B) –3 < x < 7 C) 2 <x ...

A: The negative numbers are less than 0. If a number, y is negative, then it can be written that: y&lt;...

Q: The cos'ydy is equal to 3 1 A. siny + sin³y + sin³y -; sin'y + C 5 3 B. siny – sin³y +sinsy -sin?y +...

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Q: 1. A relation R is defined on Z* × Z* by (m,n)R(p, q) → m+q = n + p . (a). Prove that R is an equiva...

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Q: 4. ( , Give a case in which |(x, y) x||yll. 5. Let X e PQ. Show that if X (1-t)P+Q, where t> 1, then...

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Q: A differential equation is given as x*- 2x + 2y = 4. dx The solution of the differential equation in...

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Q: f the integra n (x –1)

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Q: he nth term of the following sequence : -1/5, 3/8, -5/11, 7/14, -9/17

A: In the given question, the concept of the sequence is applied. Sequence A series is created by a seq...

Q: 12 If a, x and y are three non-zero and mutually non-parallel vectors, and th are given by b=x-(x-â)...

A: Introduction: The dot product between two non-zero vectors a^ and b^ are expressed as a^·b^=a^b^cosθ...

Q: (i) Show that the solution of the logistic equation dr az – br dt (3) is given by 1(t) a – br(t) r(0...

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Q: What is the general solution to the differential equation (2xy – tan(y))dx + (x² – xsec?y)dy = 0? |

A: First we have to show that the differential equation is exact. Then we find the general solution of ...

Q: Given the differential equation ye*dx + xe*Ydy – 2ydy – 2y*dx – 6xy²dy = 0 , %3D EN then what is = ?

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Q: dy \ Find for dx et dt

A: In this question, the concept of the fundamental theorem of calculus is applied. Fundamental Theorem...

Q: b) For a set X = {1, 2, 3, 4}, let P be the partition {{1,3}, {2, 4}}. The partition P induces a rel...

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Q: Question 1: Find the Nim-sequence of the subtraction game with subtraction set S= {1,2,5, 7 }

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Q: Theorem 3: Ifconverges to l, ther any subsequence of also converges to l.

A: We have given that , sn converges to l. Let , tn be any subsequence of sn. We need to prove that , t...

Q: 3.1 For the given matrix below in [3.2], without row reducing, say why the inverse exists. 3.2 Using...

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Q: 4. ( A 2-kg mass is attached to a spring with stiffness k = 18. Neglecting dampıng. write out the eq...

A: Given that: Mass of the attachment, m = 2-kg Stiffness of spring, k = 18 To find the equation of m...

Q: Q5) Choose the correct answer for the followings: i) x dy ,c is y x from point (0,0)to point (1,1) e...

A: Given the integral ∫cxdy and c is y=x from point (0,0) to point (1,1).    

Q: :Q2. Solve the following IVP using Laplace transformation y" + y' + 9y = 0. y(0) = 0.16, y'(0) = 0.

A: Introduction: The Laplace transformation is very much useful to solve a higher-order linear or non-l...

Q: Q2 FILL IN THE BLANKS. No justification is required. Let G be the following graph: 9. 10 11 12 13 14...

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Q: Determine whether the line integral of each vector field (in blue) along the semicircular, oriented ...

A: Determine whether the line integral of each vector field along the semicircular or oriented path is ...

Q: Each exercise gives a doubling time for an exponentially growing quantity. Answer the following ques...

A: The number of tumor cells is doubling every 6 months. We have to find the number of cells after 6 ye...

Q: Ture or False planar graph is a graph without loops. trees are not planar graphs. Every simple plana...

A: Since you have asked a question with multiple subparts so as per guidelines we will solve the first ...

Q: I the nth term of the follow

A: In this question, the concept of the sequence is applied. Sequence A series is created by a sequence...

Q: z = f( a, b, d, c), write the exact differential of the dependent variable

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Q: Consider the recurrence relation a, = 3a,-1- 2a,-2 with first two terms ao = 5 and a = 7. (a) Write ...

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Q: nse in Fig. if R d charge are zero

A: The voltage v(t) is calculated as  

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Q: Find the interval of convergence of the following series: x5 x7 5 +.. 7 all values of x O -2<xs2 O -...

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Q: e) Suppose that S is an equivalence relation on a set A = {1,2,3, 4, 5, 6, 7}. If 4 e [3] n [5], the...

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Q: Find the ic by using Least cost Method? Di Dz D3 Dy supply 10 20 %3D 15 12 7) 20 2, 25 14 16 18 15 e...

A:   D1 D2 D3 D4 supply S1 10 0 20 11 15 S2 12 7 9 20 25 S3 0 14 16 18 15 Demand 15 15 15 10   ...

Q: If possible, use at least three strategies to solve each of the following problems. At least two of ...

A: Observe the number of toothpicks in each case.

Q: Use mathematical induction to prove the following: 2 1+8+27+·..+ n³ n(n+1) %3D 2

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Q: Exercises 1. Show, by drawing, that the following graphs are planar: (i) the wheel W5; (ii) the grap...

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Q: . Show that dim(w,) + dim(W,)– dim(w, n w,) = dim(w, + w, - 1 C

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Q: Q4: Is this graph a planar graph or not ? k h a

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Q: z2-7z+3 Using Cauchy's Integral Formula Evaluate f ,where c is the circle Iz| = 2. z+i

A: We have to evaluate the value of the integral ∫z2-7z+3z+ιdz over the circle z=2, using the Cauchy in...

Q: Give equations for ellipses. Put each equation in standard form. Then sketch the ellipse. Include th...

A: Given,          6x2+ 25y2= 400

Q: Test for exactness. If exact, solve. If not, use an integrating

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Q: y implication, P implies Q, the contrapositive of the implication is logically equivalent to P impli...

A: Introduction: a proposition or theorem formed by contradicting and swapping the subject and predicat...

Q: Q4 Let f : R → R be the function defined by 1 f(a) = 2" %3D a) Is f is one-to-one? If yes, then expl...

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Q: Prove that if n is a triangular number, then so are 9n + 1.25n + 3, and 49n + 6. Hint: Recall that i...

A: Triangulars numbers are those which are of the form k(k+1)/2 and some examples are 1,3,6,10,15 and s...

Q: preofs H.W-

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.