The curves f(x) = x² – 2æ – 5 and g(x) = 4x – 10 intersect at the point (1,-6). Find the acute angle of intersection, in radians on the domain 0

Q: Let f(x) tangent line to the graph of f(x) at the point (0, 0) is = 6x + 15 – 15e". Then the…

A: The given curve is: f(x)=6x+15-15ex

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Q: Given that the line y= 2x +c is a tangent to the curve y = kx, where c and k are positive constants…

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Q: Find f(4) and f'(4), assuming that the tangent line to y = f(x) at a = 4 is y = -7x +2.

A: The derivative of a function at a point represents the slopeof tangent at that point .

Q: FIND THE LENGTH OF THE CURVE y = In sec X from X = 0 to X = - 4

A: Given curve is y= lnsecx .  We have to find the length of the curve from x=0 to x=π4. Length formula…

Q: Please help me find the length of the curve

A: We\'ll use arc length formula with a=pi/2, b=2pi/3.

Q: to the curve y = F(x) at the point with x %3D

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Q: 3. For f(x) =r² - 5x-6, make a table of slopes of secant lines and make a conjecture about the slope…

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Q: Find all points on the graph of x2y − 2x + 63y = 2 where the tangent line is horizontal. (Enter…

A: Differentiate the equation x2y-2x+63y=2 wrt x:  ddxx2y-ddx2x+ddx63y=ddx22xy+x2dydx-2+63dydx=0

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Q: x = e' and y = te %3D

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Q: Find the exact length of the curve. y = Vx - x2 + sin

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Q: find the tangent line to the parabola (x + 2y)^2 + 2x – y – 3 = 0, parallel to the line x – 4y = 2.

A: Given the parabola x+2y2+2x-y-3=0..............i  Determine the slope of given line x-4y=2…

Q: Since the tangent equation of f(x) = x^3 – x^2 + 3x – 5 drawn from the x = 1 apse point on it is y =…

A: Given : Function  f(x) = x3 – x2 + 3x – 5 Tangent equation on the given function f(x) at point x =…

Q: Find the points on the graph of x^2+2x+4y^2=4+y where the tangent line is horizontal

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Q: For the curve y=ax^3+bx^2+12x-7, what values of a and b will make the tangents to the curve at x=2…

A: Solution is here

Q: 1. In the open interval (0, T/2) , find the point where the slope of the curve is 4? y = tan x

A: Given function , y= tan x, we have to find at what point, slope of the the given graph is 4.…

Q: a point on the cor ve y=x² - 2x -3 at which is parallel to Find the tangent line the X-axis

A: Given query is to find the the point where tangent line paray to x axis.

Q: 8. The line y = -4x + b is tangent to the curve f(x) = 2x² – 8x + 12. Determine the value of b. %3D

A: The equation of the tangent at a point h,k on a curve y=f(x) is given by, y-k=f'(h) (x-h)

Q: Find the equation of the curve, if at any point on the curve y "= 1- vĩ and it has a tange line at…

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Q: y = -V16 – x², — х2, -4 < x < 0.

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Q: Find the lengths of the curves y = sin -1x - √(1 - x2), 0≤ x ≤ 3/4

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Q: At the given point, find the line that is tangent to the curve. 5x3y - n cos y = 6t, tangent at (1,…

A: 5x2y-πcosy=6π=ddx(5x2y-πcosy)=ddx(6π)=10xy+5x2y'+πy'siny=0=(5x2+πsiny)y'=-10xy y'=-10xy5x2+πsiny…

Q: 4 Let f(x) = 4x + x2 given by y = mx + b for . Then the equation of the tangent line to the graph of…

A: We know that if m is slope and (x1,y1) is point on line the equation of line is given as-  (y - y1 )…

Q: 1. In the open interval (0, T1/2) , find the point where the slope of the curve is 4? y = tan x

A: Given the curve  y=tan x

Q: Determine the length of the curve of the following functions (x²*+ 1)} a, y=- from x = 1 to x = 4 b.…

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Q: Find the slope of the tangent line to the graph r=2sin(0) at the point V3, 3 11.

A: We have to find

Q: 2. Consider the squiggly graph of all points (r, y) that satisfy sin(re") = a + y. 1 Using implicit…

A: Given, sinxey=x+y

Q: Find an equation of the tangent plane to the graph of f (x, y) =2x2 - 4xy 2 at (-1, 2)

A: Given: f(x, y) = 2x2 -4xy2  To find: Equation of tangent plane to the graph of  f(x, y) = 2x2 -4xy2…

Q: Find the equation of the tangent plane to the graph of the curve f(x, y) = x² + y² at the point…

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Q: Find an equation of the tangent plane to the graph y = x² + 2xz at (1,3, 1). (Possible Answer: 4r –…

A: We have to find an equation of the tangent plane to the graph y=x2+2xz at 1,3,1.

Q: Find the equation of the tangent to the curve y = cos 2x at the point where x = kko

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Q: find the slope of the curve x = e^-tcost2t, y=e^-2tsin2t at the point t= 0

A: find out the slope of the curve at t=0

Q: The x- coordinate of the point on the graph of y = Vx-1 at which the tangent line is perpendicular…

A: slope of tangent of the curve y=x-1 is dydx=12x-1 slope at (x1, y1)dydx=12x1-1=m1if (x1, y1) is the…

Q: Find the x-value(s) at which the tangent line to the curve y=(6x+1)/(ex) is horizontal. If there are…

A: Here, we need to find the x-value(s) at which the tangent line to the curve y=(6x+1)/(ex) is…

Q: If y-mx+B is thế équation of the tangent line to the curve X +2xy – y+ x = 39 at x=5 with a negative…

A: At x=5 we find y The points are (5, 1) and (5, 9)

Q: Find the tangent line to the curve (x-3y)2  + 8x + 12 = 0 at the point where y = 0

A: First differentiate at point then use equation of tangent line

Q: Find the equation of the fangent line to the graph of the function f (z) sin (3,/7) at the point…

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Q: If the length of the curve y = 4 x7 from the point (0, 0) to the point (Xo, f(xo)) is L= 1 (145)*…

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Q: Find the tangent line to the curve (x-3y)²+8x+12=0 at the point where y=0

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Q: Find all the points of the graph of y = (x - 2)2 at which the tangent line is perpendicular to the…

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Q: - Find the value of 'a' for which the tangent to the curve f(x) = (a + 2) x³ − 3ax² + 9ax − 1 never…

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Q: Find the exact length of the curve. y = (x-x2)1/2 + sin-1((x1/2))

A: The arc length formula is given as

Q: Find the slope of the tangent line to the curve y = g²+4r+7 at the point (0, 3). 7a+2 Determine da…

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Q: Graph the curve over the given interval together with its tangent at the given value of x. 37 19) y…

A: csvs

Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

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Q: Q1) Find the tangent y = vx2- x +7 at x = 2.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Find the value of 'a' for which the tangent to the curve ƒ(x) = (a + 2) x³ − 3ax² + 9ax − 1 never…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.