Show that the functions e^x , e^2x , e^3x are linearly independent.

Q: Find the slope and y-intercept of the line through the point (6,7) that cuts off the least area from…

A: The line passes through the point (6,7) that cuts off the least area from the first quadrant.

Q: Calculate the length of the tangent line, normal line, sub-tangent and subnormal from: a. xy² = 18…

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Q: Give a vector valued function whose graph is same as y=ln (x)

A: We know that a function with the representation r→t=ft i∧+gt j∧ is called a vector valued function…

Q: Find the second derivative of the funcion. y%3D

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Q: e point at

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Q: Verify by differentiation that x4 is an antiderivative of 4x3.

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Q: Use a linear approximation to estimate V65.

A: 653

Q: If X and Y have joint pdf given by

A: From the given information, fX,Yx,y=2I0,yxI0,1y                =2, 0<x<y, 0<y<1

Q: How Vector autoregressions is used for Casual Analysis?

A: The vector auto regression (VAR) model is one of the analytical techniques used most commonly in…

Q: Find the orthogonal trajectories of the family of curves.

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Q: Find the equation for the perpendicular trajectories of the curve family. 1. x -

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Q: Find the equation of the line passing through the point (4,5) and perpendicular to the line y= x+2…

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Q: Prove the relationship =<- dt

A: we have to calculate  ddt&lt;px&gt;  .....(1) &lt;px&gt;=-ih∫ψ*∂ψ∂xdx .....(2) substituting equation…

Q: Find the orthogonal trajectories for the family of curves y=c1x4

A: First of all rearrange the given equation in such a way that both the variables be on one side of…

Q: Find the derivative. using chain rule 7 5. у %3 V1-14x2

A: The given function y=71-14x2

Q: Compute the derivative of f() = arcsin(x² e3x). %3D

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Use a linear approximation (or differentials) to estimate the given number. (1.999)3

A: First I have find the linearization of x^3 near x=2 and then find the required approximated value.…

Q: Find the orthogonal trajectories of family of curves x-y=cx^2

A: To determine the orthogonal trajectory of the equation f(x,y)=c Find dydx Replace dydx→-dxdy Solve…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. rtan(x) 5t…

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Q: Find the equation for the perpendicular trajectories of the family. 1. x - curve

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Q: ¿What is a derivative of laplace transform, please define theoretically

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Q: Use a linear approximation (or differentials) to estimate the given number. (1.999)5

A: Given term is (1.999)5Let x = 1.999

Q: 28 dt dz -1

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Q: Compute da -dx

A: ∫05e-xxdx

Q: Find the equation of the line through the point (2, 5) that cuts off the least area from the first…

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Q: Find both first partial derivatives. az

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Q: Use the linear approximation to estimate

A: In this question, by using a linear approximation to evaluate the value of the expression using…

Q: Find the orthogonal trajectories of

A: Given,          y=ax2+4ax+4a, where a being paarameter.

Q: Compute the derivative of g(x) = | 1 dt. 2 1+t5 2" 1+æ15 1+25z 2" In 2 1+æ15 1+25z 2" 1+a15 1+25z 2"…

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Q: Еxample 5 1 1- Vxdx ха 0,

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Q: Show that the negative gradient points in the direction of greatest decrease

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Q: Calculate the derivative 33 dt da using Part 2 of the Fundamental Theorem of Calculus.

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Q: can we calculate the derivative of a matrix and the nth root of a matrix ?

A: Yes, derivative of a matrix and the nth root of a matrix both can be calculated.

Q: Estimate 3√9 using a linear approximation at a=8.

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Q: Choose the derivative of sec-(æ). 1 1+ 22 1 - 1 1 V1-3 1 aVa - 1 1 1+ 22 1 1 - a2

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Q: 1, cosX, cos 2X,--- , cos mx

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Q: What is the standard linear approximation?

A: A linear approximation is an approximation of a general function using a linear function. They are…

Q: The percentage of male workers who prefer a female boss over a male boss increased approximately…

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Q: Find the equation of the tangent line on 3xe™v² - ez 2ye at (1,1)

A: Given  3xexy2-ex3=2yex2first we find dydx at point (1,1)

Q: How to calculate a gradient

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Q: Give one problem for  partial differentiation of function of U with respect to 3 independent…

A: It is partial derivative problem

Q: Find the derivative. (Hint: do chain rule. ) * 12° dt 6x 8x6 12x/2

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Q: Calculate the length of the tangent line, normal line, sub-tangent and subnormal from: a. x²+ y²-4x…

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Q: The function f (x) = ax³ – bx² has a gradient of 2 at point (1,6). Find its gradient when x = 2.

A: Given  f(x) = ax3-bx2

Q: How can one use a vector-valued function to represent a curve in two dimensions?

A: a plane vector consists of two quantities: direction and magnitude. Given any point in the plane…

Q: Find the complete or particular rential equations:

A: Introduction: The rate of change of a function at a point is defined by its derivatives. The study…

Q: (In iny

A: To find the derivative of the given function- lny=lnxylny Here we will use the following formulas-…

Q: End fz(3) in terms of the joine pdf of X and Y if

A: From the given information, Let, f(x) be the density function of X. f(y) be the density function of…

Q: Find the derivative. USING CHAIN RULE 4 y = V3x² – 5x + 2

A: