Determine whether each set equipped with the given operations is a vector space. For those that are not vector spaces identify the vector space axioms that fail. The set of all 2 x 2 invertible matrices with the standard matrix addition and scalar multiplication. V is not a vector space, by Axioms 5 - 8 fail to hold. V is a vector space. O V is not a vector space, by Axiom 9, 10 fails to hold. Vis not a vector space, by Axiom 1 fails to hold. V is not a vector space, by Axioms 2, 3, 4 fail to hold.

Q: Evaluate the function for the given values of x. h(x)= Part 1 of 5 h(-3)= Part 2 of 5 -5x+7 for x…

A: The given function,   hx=-5x+7for x≤-23x+2for -2<x<34for x≥3

Q: Q31 Find the Laplace Transform to the following function L sin2t cos3t

A: Solution is given below:

Q: The carbon monoxide level in a city is predicted to be 0.02x3/2 + 1 ppm (parts per million), where x…

A: The function is P(t)=0.02(12+2t)3/2+1

Q: Use the Limit Comparison Test to determine if the series converges. k³ +7 k(k+ 3) (k − 2) (k+1) k=1…

A:

Q: Q4\Use Cramer's Rule to find the values of x, y, and z from the following equations: 2x + 3y - z = 1…

A:

Q: (A) 3y²ex+y²dx (B) 3) [3y²e²+ y² dx 0

A: In both integration we have to integrate with respect to x . So we treat y as a constant & solve…

Q: The vectors a = : (4, -10, 8) is perpendicular to the vector b = (8,-8, -14). Select one: True O…

A:

Q: 2. Imagine you were given three different tables of values; a linear, quadratic and exponential one.…

A: Imagine you were given three different tables of values; a linear, quadratic and exponential one. To…

Q: Let a be a real number. Evaluate the following integral: So f +ydady

A:

Q: Find the area between the curve on the given interval  y= x^3 , y= x^2-1, 1 < x < 3

A:

Q: The strength of a patient's reaction to a dose of x milligrams of a certain drug is R(x) = 4x√11…

A:

Q: dy (8) The solution of differential equation: + y = xy³ is dx (a) = x + ²+ce²ª, y (b) = x² + + ce²x,…

A: Using differential equations

Q: Which of the following is the equation of a sphere with radius r = 3 centered at the point…

A: Given that radius of the sphere is 3 and the center of the sphere is -1,0,-2. We have to find the…

Q: 2. (x² + y² + 1)dx + x(x − 2y)dy = 0

A:

Q: 2. find the derivative of the function g(x, y, z) = 3e* cos yz ,at the point P. (0,0,0) in the…

A:

Q: Given the points A(-8, 2, 3) and B(-8, 2, -4). Question 3 a). Write parametric and symmetric…

A:

Q: Find the root's 51 of Complex equation:

A: Given:      5√(-1)

Q: 27. Consider the function h(x) = 2x² e-x² a) In two or three steps, write the properly simplified…

A: As per our guidelines, we are supposed to solve only 3 subparts. Kindly post other parts in the next…

Q: 3 A line passes through the point (-6, 4) and has a slope of 2 Write an equation in slope-intercept…

A:

Q: Sxe 2x dx

A: Integration by parts: ∫u·v dx = u·∫v dx - ∫ddxu·∫v dx dx   We have to evaluate ∫x e-2x dx.

Q: Find the distance from the point (3,-7,-1) to the plane -x + 5y + 2z = 34.

A: Here is the solution:

Q: 2. find the derivative of the function g(x, y, z) = 3e* cos yz ,at the point P. (0,0,0) in the…

A: We have a given function g=3e^x cos(yz)

Q: 46×12

A: Find value of 46×12

Q: f sin²(x) cos²(x) dx

A: cos(2x) = 1-2sin2(x) = 2cos2(x)-1. ∫cos(ax) dx=1asin(ax)+C ∫xn dx = xn+1n+1+C

Q: 1. If y = sin x² x =²), ex find dy dx

A: Given y=sinx2-xex To find dydx

Q: Let a be a real number. Evaluate the following integral: Sofyx + y dxdy y-1

A: This question is related to double integration, we will solve it using given information.

Q: (m) X + x + 1 dx Oseparable exact Olinear in x Olinear in y homogeneous Bernoulli in x Bernoulli in…

A:

Q: Approximate the change in the volume of a sphere when its radius changes from r = 40 ft to r=40.1…

A: We have to given volume of sphere in term of r

Q: The graph of f-1 is given below. Graph the tangent line to f-1 at the point P(6, 1) for f(x) = -x² +…

A: Let's solve.

Q: Please recheck it, the answer is wrong. It isn't 823.

A:

Q: 3. Let Compute each of the following IV. B-¹αoß a = B = 12 2 3 2 3 1 + 4 4 5 6) 6 3 54 2 3 1 2 4 4 5…

A:

Q: \(\) The vectors u= 8> and v= are not orthogonal if and only if -136 Select one: O True O False

A:

Q: Q4\Use Cramer's Rule to find the values of x, y, and z from the following equations: 2x + 3y - z = 1…

A:

Q: S In (x) √xln(x)-x -X dx

A: ∫ln(x)xln(x)-xdx

Q: dy Find where y = csc dx Provide your answer below: dy dx = +9). 6x + 9

A: y = csc-(1/(6x+9)) find dy/dx = ?   here we use formula  dcsc-x/dx = -1/xx2-1   using this formula…

Q: 3. Find the solution of the following system of liner inequalities by graphing: (K + 2y > 5x + 3y…

A:

Q: x fare cos = dx 2

A: Indefinite Integration

Q: Given d = and v= -5d +30=< find-5d +3v..

A: The calculation follows easy.

Q: a = 6i + 4j + 8k and b = 9i – 6j + 12k. a) [ and b are orthogonal, parallel or neither. b)[ >]…

A:

Q: The length of the curve r = sin² for the period 0 ≤0 ≤π is 6 O 2 O 8 O 4 O O None of them

A: Use derivative and length of curve formula for polar curve.

Q: (a)[1 Show that the following equation represents a sphere, and find its center and radius. x² + y²…

A:

Q: Ted's Machine Shop purchased a computer to use in tuning engines. To finance the purchase, the…

A: topic - compound interest

Q: In Bernoulli equation y' - xy = xy³, the value of 1(x) is ex² False True O

A:

Q: 100 The value of p for the series Ση=1 2n | n! by using ratio test is -1 8 N 2 0 1 O

A:

Q: Use the Modified Euler method to approximate the solutions to each of the following initial-value…

A:

Q: (a) Use the Midpoint Rule with n = 6 to approximate integral 8 x-6 So dx 6 x+8 Write your answer…

A:

Q: f(x, y) 4xy; R is the region bounded by the graphs of y = V1 - = x² and y = 0 for 0 ≤ x ≤ 1

A: Solution is given below:

Q: O a = 5i - 4j + 3k and b = 15i 12j + 9k. -

A:

Q: Find the length of the curve for the interval 1 ≤ x ≤ 9 3 = √ √ √ ² ³ - 1 d dt 1 Select the correct…

A:

Q: .1 The evaluation of 2xe³ dxdy is 3e-1 O e-3 -1 e- None of them O -3e O

A: To find out the double integration.