given the function h(x) = - x/2 + 1 calaculate the values of h(-2) and h(3)  and draw a graph.

Q: . Show that if S is a subbasis for topologies T1 and T2 on a space X, then T1 = T2.

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Q: The value of x that satisfies f(xr)= 0 is called the (A) root of an equation f(x)=0 (B) root of a fu...

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Q: JD x, t(3lxg-19メーのメ4ニ630 19 Xq -91 Xq - || X, t 22 Kg t 20 Xg t 12 X4 Il X, - 2| Ka -19 xg - 30 Xq -...

A: The given system of equations are:-10X1+31X2-19X3-91X4=630-11X1+22X2+20X3+12X4=61211X1-21X2-19X3-93X...

Q: Consider the following system of lincar equations: I1 + 3r2 2r1 + 6r2 + 13 4r. -1 I3 - 6r4 = 2 2r3 +...

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Q: Determine the Laplace Transform of cos(2/3t) cos (V31) Note:

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Q: 2. Consider the following set of constraints: x, + 2x, + 2x, 2x, - x, + x, + 2x, 5 8 4x, - 2x, + x, ...

A: (a) After introducing slack variables we have Max Z = 3x1-x2+3x3+4x4+0S1+0S2+0S3subjected tox1+2x2+2...

Q: Evaluate, (z1 + z2)^2 Select the correct response: (z1)^2 + (z2)^2 - 2 z1 x z2 (21 + z2) (z1 – 22) (...

A: Concept: Here the following identity is used: a+b2=a2+2ab+b2 where a and b are any variables.

Q: 6. Using the Newton's backward interpolation formula construct an interpolation polynomial of degree...

A: Newtons Backward difference formula table x y ∇y ∇2y ∇3y -0.75 -0.0718           0.0471     ...

Q: 14. Fill in the squares using the digits 4, 5, 6, 7, 8, and 9 exactly one time each to make the smal...

A: In this problem, 6 digits are given. We have to make two 3-digit numbers using those exactly once.  ...

Q: Solve the following equations in Z6 with x expressed in both standard and non-standard names: (i) xx...

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Q: With initial guess of 0.75, what is the value of one real root of f (x)=Dx' +5x-5 using Fixed-Point ...

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Q: 4. Prove that 13 1 13 1 < cos(1) 24 - 1440' 24 where 1 is in radians. 720

A: Solution

Q: 3. A company that operates 10 hours a day manufactures two products on processes. The following tabl...

A: Solution

Q: Find the Laplace transform of the solution to the following initial value problem y + y = f(t), y(0)...

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as ∫0∞e-...

Q: Determine the percentage relative error (In 2 decimal places) when we compare the derivative of 12e2...

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Q: Somie, a leader of the underworld, was killed by one of his own band of four henchmen. Detective Sha...

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Q: prove that (1, 6) 13 an o pen set 13 an open çet.

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Q: Simplify (vZcis (음찌))*(2cjs (-즐))" 증))* 8 5 (2cjs (–

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Q: Let V be the vector space over the field of real numbers consisting of all real-valued sequences (a1...

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Q: 5. A third degree polynomial passes through the points (0, – 1), (1, 1), (2, 1) and (3, – 2). Determ...

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Q: 16. (i) Is the binary operation a *b = a + b – ab commutative for all real numbers a, b? (ii) Is the...

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Q: Find the general function M(x, y) so that the equation is M(x, y) dx + (sin xe ^y + xy) dy = 0

A: The given equation is M(x,y)dx+(sinxey+xy)dy=0We have to find general function M(x,y) Exact Differen...

Q: Suppose that the only barrio is located at the center of a circular field. If a researcher needs to ...

A: (a) We know that distance between two points O (x1 , y1)   and   A(x2, y2) is given by formula, d=di...

Q: TRUE OR FALSE If p is true and q is false then find the truth value of "p and not q" If p and g are ...

A: Solution : a)  Given that  p is true and q is false =&gt;  not q is True     The truth value of " p ...

Q: 2. 27x + 6y - z = 85, x+y + 542 = 110, 6x + 15y + 22 = 72.

A: Given system of equations is27x+6y-z=85x+y+54z=1106x+15y+2z=72Here the coefficient matrix of the giv...

Q: Use the graph y=g(x) to graph the given function. 12- 6- -12 -9 -6 -3 12 -3- y = g (x) -6- -12- y=5g...

A: Given: Let us use the given graph y=g(x) to graph the given function y=5g(x)

Q: 2. Find the sum of the coefficients of the polynomial obtained by fully expanding (x - 2). С. 1 А.-2...

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Q: If M = 4320 and G = 150, what is the AD curve? A. 4320 Y =: +1130 2x4320 + 1130 %3D P. Y = 2x4320 %3...

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Q: 4 3 1 let A = -1 1 -3 Find a basis for the eigenspace corresponding to the eigen- 4 9. value A= 3

A: given  A=423-11-3249 find a basis for the eigenspace corresponding to the eigenvalue λ=3

Q: What is the approximate derivative of f(x) = x2e* , using backward-difference approach at %3D x-2 an...

A: The main objective is to calculate the value of the derivative of the function f(x)=x2ex at the poin...

Q: Show that the groups Z8xZ20xZ12 and Z120xZ4xZ4 are isomorphic by define a one-one and onto map? what...

A: We will use the basic knowledge of groups and abstract algebra to answer this question.

Q: 1. Determine whether each of the following sequences converges uniformly on [0,+∞). a. fn(x) = x"e-n...

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Q: What 3-digit number has the number 5 as its digit in the tens place and the digit in the hundreds pl...

A: The digit in the tens place is 5. Consider the number is x5y. The digit of the hundreds place is twi...

Q: Using the Fixed - Point Iteration, find the iterative value at the third iteration of x -3x +1 = 0, ...

A: We have to find iterative value of third iteration.

Q: 1. bg {a, b, {c}} 2. b e {a, b, c} 3. {b} € {a, b, c} 4. (b) c {a, b, c} 5. {b} c {a, b, {c}}

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Q: Evaluate (5+ i sqrt (3)) / (1- i sqrt (3)) Select the correct response: ½ + (3 sqrt (3))/2 i ½ + i s...

A: To evaluate the given expression. 

Q: b) Find the area under the curve given by g(x) = x? + 4x between x= 6 and x = 9.

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Q: 1. Use the Lagrange's formula to find the quadratic polynomial that takes these values 1 Then, find ...

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Q: 4. Determine if the equation is exact, and if it is exact, find the general solution. a.) (y² + 2t) ...

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Q: Consider the Sturm-Liouville problem Sy" + (1+ X)y = 0, A2-1. y(0) = 0, 3(1) = 0 (a) Is A = -1 an ei...

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Q: 3. Given the following system: x, - 2x, + 2x, + 3x, = -1 -3x, + 6x, + x, + 5x, =-11 2x, %3D 4x, 2x, ...

A: Given: Let us consider the given systems, x1-2x2+2x3+3x4=-1 -3x1+6x2+x3+5x4=-11 2x1-4x2-2x3-6x4=10 (...

Q: -x+3 () Answer the following questions, given the equation y = -2 a) Graph the function using a suit...

A: Given equation is y=-214-x+3+1 We have to answer the following question. a)Graph the function using ...

Q: A population grows according to an exponential growth model, with Po = 70 and P 133 %3D Complete the...

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Q: Draw a regular octagon (8-sided polygon) in Using your protractor, measure the interior and exterior...

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Q: 19. Druid city is currently selling Lamplighter IPA in their taproom for 2, the marginal cost of pro...

A: Given: Druid city is currently selling Lamplighter IPA in their taproom for 2, the marginal cost of ...

Q: 6. The diagram below shows a rectangle inscribed in a right triangle having a base of 12m and a heig...

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Q: 1. a 2 b 4

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Q: (II) [1 pt.] Repeated root. Solve this IVP: y" – 4y' + 4y = 0, y (0) = 3, y' (0) = 0

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Q: acuce 4. Given J(5, 0), K(8, –11), L(-3, –14), M(-6, –3), determine whether parallelogram JKLM is a ...

A: Given  here we have given the coordinated of the parallelogram J(5,0), K(8, -11), L(-3, -14), M(-6,-...

Q: Let F be a collection of subsets of a set X. Then the intersection A of all o-algebras of subsets of...

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.