Find the equation of the normal line of f(x) = x⁴ + 2x at x = 1 using the limits definition.

Q: Find the implicet differentiation x3y3-y=x

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Q: ) Estimate the value of Csc (0. 2) using linear approximation and without using any kind of…

A: Given problem:- Estimate the value of csc(0.2) using linear approximation

Q: S(r) = In (r² + 2x + 5)

A: SOLUTION-

Q: The integrating factor of the LDE y' = x - 2ycotx is

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Q: How can we minimize the error of an approximation in a linear approximation at the point (a. f (a))?…

A: Query- How can we minimise the error of an approximation in a linear approximation at the point…

Q: Find the equation of the normal line (NL) to the graph f(x)=x³ – 4x atx = 3 .

A: We need to find derivative.

Q: At waht x does f(x) have a local(relative) maximum?

A: A function f(x) is defined for x values there are local maxima and local minima in the given curve.

Q: Find the normal lines to the curve xy + 2x - y = 0 that are parallel to the line 2x + y = 0.

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Q: 4) Find the orthogonal trajectories of the family of curves

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Q: Find positive numbers x and y, whose sum is 75, such that xy2 is maximized.

A: Positive numbers x and y,x+y=75xy2 is maximized

Q: Find the normal lies to the curve ru + 2x – u = 0

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Q: Find the equation of the normal line of y = 8 – x³ at (-1 , -3) а. 8-Зу — х %3D 0 b. х— Зу — 8 %3D 0…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the critical points of the function f(x,y) = y² + x²y+ x² – 2y and use Second Derivative Test…

A: Finding fx, fxx, fy,fyy and fxy and use D(x,y) = fxx . fyy - fxy^2 , to find relative maxima or…

Q: Find the slope of the curve y=x2−3x−4 at the point ​P(2​,−6​) by finding the limiting value of the…

A: Giveny= x2-3x-4 = f(x)at point ( 2, -6)as f(x) =x2-3x-yand f(2+h) = (2+h)2-3(x+h) -4…

Q: Consider the following information fz(x, y) = 2xy - 2r³ and f₁(x, y) = x² + y² – 6. Use the Second…

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Q: What is the equation of the normal line to the curve x2 + y² –6x- 2y=0 at (2,4)? A x+3y+10= 0 B…

A: The given curve is x2+y2-6x-2y=0...(1) To find the equation of the normal line to the given curve at…

Q: Find the equation of the normal line in the curve x2 − 6x + 2y − 8 = 0 at x = 3

A: We need to find equation of normal line.

Q: Find the two points on the curve (xy)² = 2 – xy where the slope of the normal line is I.

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Q: What is the equation of the normal line to the curve x2 + y2 - 6x-2y=D0 at (2,4)? none of the given…

A: Given curve is: x2+y2-6x-2y=0To find equation of normal to curve at (2,4), we need slope of line at…

Q: Find the equation of the normal line to the graph y= x In x that is perpendicular to the line x - y…

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Q: Find the average rate of change of the function over the given interval. y =V4x + 1; between x 2 and…

A: To find the average rate of change of function y=4x+1 between x=2 and x=12

Q: Determine the equation of the normal line at the given x-value. 1) g(x) = sinx , x = 3? 4 2) f(x) =…

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Q: 4. At what point on the curve x = y² – y will the normal line cross the y-axis at y = 8?

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Q: The pdf of a continuous RV X is given by f(x) = 3x², where () < x < 1. The median Q2 of X equals

A: Given :-   fx = 3x2                      0&lt;x&lt;1we have to calculate the median   now ,…

Q: Find the equation of the normal line to the curve y = 2x - x at (2, 0). O a. 2x - y = 4 O b.x - 2y =…

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Q: Find the critical points of the functions S(x, y) = x + 2y – 4y + 8x, g(x,y) = x² – 14xy + y Use the…

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Q: What is the marginal PDF f(x)? What is the marginal PDF f(y)?

A: The PDF f(x) is:…

Q: 4. Find the orthogonal trajectories of the family of curves: y = ke* %3D

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Q: Find the equation of the normal line to the curve f (x) = 6e2x cos x at the point (0,6). %3D

A: Now point on the function is (0,6 ) . Step 1 : find the value of the derivative at x=0 . So, f(x) =…

Q: Find the marginal PDFS fx (x) and fy(y).

A:

Q: Find the equation of the normal line to the curve y = x³+ 3. at (1, 4). %3D O a. x = 1 O b.y = 4 O…

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Q: Find the equation of the normal line to the graph of ey tan(xy) − ln(x2 − 4y) = sin2(πx) at the…

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Q: The average rate of change of fx) = ax' Over the interval osxs1 IS a

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Q: What is the equation of the normal line of f(x) = ln(x² – 3) at the point x = 2 ? %3D

A: Given:fx=lnx2-3  at a point x=2

Q: What

A: The correct option is (B).

Q: Find the critical points of the function f(x, y) = y² + x?y+x² – 2y and use Second Derivative Test…

A: Follow the steps below to yield the result . Calculate . Find the critical point by solving the…

Q: What value of a makes ƒ(x) = x2 + (a/x)have a local minimum at x = 2?

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Q: Find the equation of the normal line to the curve y = x3+ at (1, 4). O a. y = 4 O b.y = -4 OC.x = -1…

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Q: The equation of the normal line to the curve x^2 + y^2 - 6x + 10y + 29 = 0 at (2, -3) is 2x + y = c.…

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Q: What is the equation of the normal line to the curve x2 + y² – 6x – 2y=D0 at (2,4)? A 3x-y+10=0 B…

A: We need to find the normal line to the curve: x2+y2-6x-2y=0 at (2,4) This can be done as follows:

Q: ) Use the second derivative test to classify each critical point of f (x,y)=-x' +4xy- 2y² +1 as a…

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Q: What is the equation of the normal line to the curve x2 + y² - 6x - 2y=0 at (2,4)? A x+3y- 10 = 0…

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Q: Find the critical point of the function f(x, y) = 24x – 4y² – In(|x + y|). - - c = Use the Second…

A: see below the answer and explanation

Q: Find local max min and saddle points of f(x,y)= x^3-3x+3xy^2

A: Given function is f(x,y)=x3-3x+3xy2

Q: What is an average rate of change of function f(x) over the interval [1, 6]?

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: What is the equation of the normal line to the curve x2 + y2 – 6x – 2y=0 at (2,4)? (А) х+3у-10%3D0…

A: Please refer the attached image for complete solution. THANK YOU.

Q: What is the equation of the normal line to the curve x² + y² -6x- 2y=0 at (2,4)? A none of the given…

A: The given curve is x2+y2-6x-2y=0 at 2,4. We know the equation of the normal line is: y-y1=-1mx-x1…

Q: Use the Second Derivative Test to determine the relative extremum trema) and saddle point(s), if…

A: This is a problem related to maxima and minima of the function. By first derivative test we will…