16 (ii) 8. 25 mDAS

Q: If x1/2 =(42)1/24 then find the value of x

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Q: ', Test for convergence the series 211 312 4N3 5V4

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Q: the sum of the angles of a triangle

A: The sum of the angles of any triangle is 2π i.e. 180°

Q: Exercise Find ker f and Im f for f: (S3,0)→(Z2, +) such that so if x is evev permutation f(x) =} 1 i...

A: Ker(f ) is the set of all those elements of S3 which map to identity element of Z2  i.e ker (f) = { ...

Q: If A = 40ej120°. B = 20Z140°, C = 5 + 2i, solve for A + 2B + C in rectangular form. %3D %3D

A: Here i=√-1. Sometimes j is used instead of i.  

Q: Fix a point P on the line ( and let N be normal unit vector to (. Show 5. (. that if N' is another u...

A: Given: A fixed point P on the line l. An unit vector N normal to l.   To show: If N' is another unit...

Q: Define a sequence by recursion An + an+1 an+2 = with initial conditions aj = ì, a2 = µ where 1, u E ...

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Q: Which of the following is NOT proportion? * A. 25:100= 1:4 B. 7:8= 21:24 C. 9:12= 3:4 D. 13:26= 1:3

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Q: Solve the following differential equation using determination of integrating factors: 2y (x2 - y + ...

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Q: Determine whether x= (0, ,0) is an optimal solution to the following linear program. maximise 3x1 + ...

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Q: Let {a,} be a decreasing sequence with a, O such that lim a, = 0. Choose all the correct statements:...

A: We choose the correct statements.

Q: 9.5. If s1 = a+ib¡ and s2 = a2+ib2, and s1s2 = use the fact that r= Va² +b² and (a¡a2 – bjb2) +i(a¡b...

A: The given problem is to show the given sum and product of two complex numbers in terms of polar coor...

Q: 2. For the set of equations 2x, + 5x, = 1 2x, + x, + x, = 1 3x, + x, = 2 (a) Compute the determinant...

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Q: 3 -6 Let A = Construct a 2×2 matrix B such that AB is the zero matrix. Use two different nonzero col...

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Q: Evaluate the unoriented line integral (2æ² + y² + z²) ds along the parametric curve a : [0, 1] → R³ ...

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Q: Solve the boundary value problem. y"+ y = x2 + 1, y(0) = 5, y(1) = 0

A: We solve the given boundary value problem  y"+y=x2+1.......(1) y(0)=5,y(1)=0

Q: 1. Find the Fourier Sine Series for f(x) = sinx (0 < x < n ) %3D

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Q: Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is inconcl...

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Q: 6. Let f: A R be a continuous function. Show that if A is compact then sup f(A) e f(A).

A: Sup(A) under the continuous function

Q: (a) Solve the following linear equation by Cramar's rule:- x - y + 2z = -4 Зx + у — 4z %3 -6

A: # We are entitled to solve one question at a time, please resubmit the other questions if you wish t...

Q: Show that the surface area of the solid region bounded by the three cylinders x² + y ^ 2 = 1, y ^ 2 ...

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Q: Q2. Let a b c A =|d e g hi f Assuming that det(A) = -7, find (a) det(3A) (b) det(A) (c) det(2A-) a (...

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Q: Fourier Series: f(x)= -x^2 + 5 , [-2,2]

A: The given problem is to find the Fourier series expansion of the given periodic function. Given peri...

Q: Find Z in (1-j5) 2= tanh cos lat5 express in lagarithm Form

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Q: 1. Show that -p → (q → r) and q –→ (pVr) are logically equivalent without using a truth table.

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Q: (5) Consider the set T= {(-1)"(1-): n E Z4). (i) Show that 1 is an upper bound for T. (ii) Show that...

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Q: Express the sum of integrals as an iterated integral in polar coordinates: r2V3 r4+V16-x² x dx dy + ...

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Q: Let f and g be functions that are continuous on [a, b] and differentiable on (a, b). Show that there...

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Q: (d) Work through phase 1 step by step. e) Construct the complete first simplex tableau for phase 2. ...

A: The complete solutions are given below

Q: [1 27 3. Let A = 1 3 Let the vector space V consist of all 2×2 matrices а X : с d b such that AX = X...

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Q: If the bank advertises its rate as 6.2% compounded monthly, and another bank advertises its rate as ...

A: Given:  Bank A gives the rate of interest at 6.2% compounded monthly. Bank B gives the rate of inter...

Q: Find the volume of the solid generated by revolving the region bounded by the curves y=x^2 and x=y^2...

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Q: A stone is tossed into the air from ground level with an initial velocity of 30 m/s. Its height at t...

A: Please see the attachment

Q: True or false? In each case, justify your answer with a proof or a counterexample (all variables rep...

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Q: The cost C of manufacturing transformers in a factory varies with the output N per day according to ...

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Q: tain the principle root of JZ rectangular form 3-j4

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Q: 2. Reduce to the form a + bi: d. sinh (3 + 4i)

A: To reduce sinh(3+4i) in the form a+bi.

Q: onsider the following two ser 00 Σ X-1 X-1 and B= > n=1 n=1 /hich of the following statements is TRU...

A: Here A = ∑n=1∞x-1nn If the series is convergent then limn→∞an1n  &lt; 1⇒ limn→∞x-1nn1n &lt; 1⇒ x-1 &...

Q: Show that the hypotheses: It is not weekend today and it is gloomy than yesterday. (¬WAG) We will go...

A: We first see that not gloomy and sunny or not sunny and glooomy are equivalent.  i.e., ~Gloomy ≡Sunn...

Q: Choose the correct answer to the question below: * Which of the followingis logicallyequivalent to -...

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Q: Prove that the difference between the square of any odd integer and the integer itself is always an ...

A: We have to prove that the difference between the square of any odd integer and the integer itself is...

Q: The equation of a plane is (X,Y,Z)= (1,0,0) + s(-1,0,-1) + t(-1,2,0),s,t ER. Determine the vector eq...

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Q: 1. Using the definition, not the table, find the Laplace transform of the function f(t) shown below....

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Q: The swimming pool can be filled with water in 10 hours using 6 hoses. How many hoses are needed if y...

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Q: 니[u(1-4) (?6-16 6)] = e-4s 2 8. (s-6)² (s-6)3 6e 4-In 6) 8. (s-In 6)3 (s-In 6) 64e-4s 2 16 (s-In 6)3...

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Q: The Maclaurin serles for f(x) = x²elz) is: (-2)*z*+2 (b) 00 (e) None (2)-kyk+2 2(k)xk+2 (c) 2kyk+3 (...

A: Any function which is differential then the function can be written in the polynomial  A Taylor  ser...

Q: Show how an improper integral having an integrand f(x) with a pole x0 is regularized as a Cauchy-pri...

A: Cauchy principal value, is a method for assigning values to certain improper integrals which would o...

Q: x) = 3c³ -3x² + -3 at x= - 1?

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Q: Solve the folloong ODE-IVP wang Euler's methed. h=0-2 Solve between vzD to Z 0-6

A: Find the approximation function value, using Euler's method of differential equations

Q: -. Which coordinate plane is closest to the point (7, 3, 8)? Find an equation of the sphere with cen...

A: we have to find the coordinate plane that is closest to the point 7,3,8 and also find the equation o...