If g(g(x)) is continous at 0, then g(x) is continous at 0.  True or False?

Q: Find the limit, if it exists. V(t + 25)(t – 1)² lim 11t - 11 t-1+

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Q: Find the critical numbers of the function. f(x) = x² log,(x? + 2)

A: fx=x2log7x2+2⇒fx=x2logx2+2ln7      ∵logab=logblna Critical numbers are the values of x for which…

Q: The function f(x) = 2x 36x + 210x – 4 has two critical numbers. The smaller one is x = and the…

A: Thw critical points are given below

Q: Disprove the statement ln x / ln y = ln x - ln y,  by, a) Letting y equal a positive constant of…

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Q: The function f(x) = 2x 30x + 126x – 6 has two critical numbers. %3D The smaller one is x = and the…

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Q: find the absolute maximum and absolute minimum values of ƒ over the interval. ƒ(x) = (4/x) + ln x2,…

A: Given,

Q: Find the domain and all critical points in the domain y=ln(x-5)

A: Domain: (5,∞),{x|x>5}

Q: • Show that both of the functions f(x) = (x − 1)^4 and g(x) = x^3 −3x^2 + 3x+ 2 have stationary…

A: given functions fx=x-14gx=x3-3x2+3x+2 (A) to show both have stationary point at x=1 differentiate…

Q: Show that the linearization of ƒ(x) = (1 + x)k at x = 0 is L(x) = 1 + kx.

A: The given function is

Q: Find the value of a so that the function f(x) = xe has a critical %3D point at x = =D3. NOTE: Enter…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = ln(x2 + 5x…

A: The given function f(x) = ln(x2 + 5x + 13),    [−3, 1] Differentiate with respect to x…

Q: When we introduced the quotient rule, we didn't actually prove it. Let's do that using only the…

A: Given Data: Function: fxgx=fx·gx-1   The chain rule for derivative is, ddtfgt=f'gtg't ......1   The…

Q: 1. Find the critical points of the function 2 f(x, y) = x² + 4xy.

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: In the function:  f(x)= (3x^2)ln(x) , x>0 What are the inflection points of the function?

A: To find inflection points of the function we need second derivative of the function.Use product rule…

Q: 1. Find the roots of the given equation where f(x) = 0 with the stopping criterion of 0.001. f(x) =…

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Q: Is ƒ(x, y) = x2 - xy + y2 - 3 more sensitive to changes in x or to changes in y when it is near the…

A: Partial derivative of f w.r.t a variable is the indicator of the sensitivity of f towards that…

Q: The derivative of f(x) with respect to x is the function f'(x) and is defined as f'(x) = lim 0…

A: To find f(x+h) replace x by x+h in f(x).

Q: True or false: The maximum value of the function y = -2 cos x + 5 is 7.

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Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Answer

Q: In the function:  f(x)= (3x^2)ln(x) , x>0  What are the critical numbers of the function?

A: Given function is

Q: x? Find the critical points of the function: f(x)= x- 2

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Q: 3. The slope of the tangent line to f(x) = A tan(¤) is 1/2 when z = 2n/3. Deter- mine the equation…

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Q: True or false: The maximum value of the function y = -2 cos x + 5 is 7.______

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Q: Find the positive critical point of the function f(x) = : 8+6 * x =

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Q: 1) The derivative of f (x) = e2x² cos x is: 2) Simplifying the expression e n(4x-3) + eln 2x In(e3x)…

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Q: 3- Show that this function is differentiable for all and find its derivative (2) = f(x+ jy) = x*-…

A: The necessary and sufficient condition for a complex function f(z)=U+iV  (where U,V are the real and…

Q: Solve for Elimination of Arbitrary constant given problem is x^2y=1+cx

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Q: 3. Use derivatives to find the critical points anc (a) f(x)= x³ – 9x2 + 24.x + 5

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the critical numbers of the function. f(x) = x³ + x?

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Q: %3D Apply the Chain Rule to find the tangent line to f(x) = 4v2x- 6e2-*at x = 2

A: We want to find the tangent of the given function at x=2 We know that slope of the tangent at a…

Q: . (a) Find the critical numbers of . f (x) = x 4 (x -1 )3(b) What does the Second Derivative Test…

A: (a) We say that x=c is a critical point of the function fx if fc exists and if either of the…

Q: • Find f (x) of f(x)= by using the definition of the x-1 derivative. • 1- Find if y=3t-4 and t Vx+…

A: we have to find the derivative using definition. as per definition  f'(x)=limh→0f(x+h)-f(x)h

Q: xsin 1x Vx+1 2tan-x Vx+1 2tan-1x QI) Find of y=: e2x+1

A: We will find dy/dx as following .

Q: The function g is differentiable, and the tangent line to the graph of y = g(x) at x = –2 is y = 2x…

A: Note that the slope of the line y=2x-2 is 2. Given that the tangent line to the graph of y=gx at…

Q: 19. Solve for A and B so that g(x) has a limit at both x = -1 and x = 3. 4x - 2, X> 3 g(x) Ax + Bx +…

A: To solve for A and B so that gx has a limit at both x=-1 and x=3. gx=4x-2,       x≥3Ax2+Bx+2,…

Q: for the funciton f(x) = x^3 - 75x Its local maximum  is____, which occurs at _____> Its local…

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Q: Let f(x) = 18xe - 1s. (a) f'(x) (b) Solve f'(x) = 0 to determine the critical values of f.

A: Recall: (uv)'=u'v+v'u

Q: 13.Find a sinusoidal function with a maximum value of 9 that occurs at x=4 , and a minimum value of…

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Q: 4)Find the inflection points of the function . f(x)=ln(x^(2)+1)

A: In this question we will find the point of inflection   we have given function   f(x)=ln(x2+1)…

Q: What is the critical point of the function g (x) = (x ^ 2/2) + x (ln (x) −1), using Newton-Raphson,…

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Q: 22) The critical points of the function F(x,y) = x³ + 3xy + y3

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Q: Find all critical points for the function f(x)= x²e!-2¤. %3D

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Q: Let f(x) = (2 – x)° f(x) has one critical value at A = | 0

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Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

A: To determine the linearization for the function.

Q: 3z2+x 30. If z – xz – y = 0, prove that- =- ax dy (3z²–x)³*

A: Let's find.

Q: Use algebraic methods to determine the critical value(s) of f(x) = x √4−x.  Give your answers in…

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Q: 5x−12/x^2−x−42 has vertical asymptote(s) at x=

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Q: find all critical points of the function f (x) = xe^2x

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Q: The value of Wronskian of two functions y, =7* and y2 =7** is

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Q: 25 p1 3) Compute f(x)f'(x) dx where f(x) =x +2, using the Composite Trapezoidal 2 rule, your results…

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.