Q: The line y = 3x + k is tangent to the curve y = x when k is equal to
A: Given, The line y=3x+k is tangent to the curve y=x3
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Q: Find an equation for the tangent line to the parabola y = x² at the point P(1, 1).
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Q: For what value of x does the tangent line to the curve y=7+3e^x−6x is parallel to the line 8x−8y=9?
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Q: 2. Find the tangent lines to the curve y = x4 – 14x2 + 17x + 40 perpendicular to the line x = 7y +…
A: Given, y=x4-14x2+17x+40 Now differentiate with respect to x we get, dydx=4x3-28x+17 The tangent is…
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Q: Find the equation of the tangent line to the curve y=2sin(x) at the point (pi/6, 1) in y=mx+b
A: Using equation of tangent formula.
Q: 5. Find the equation of the tangent and normal lines to the curve x = t2 – 2t, y= t3 - 3 when t =…
A: Firstly we find Slope of tangent and slope of normal to the given curves and then we will find…
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Q: What is the slope of the tangent line that touches the graph of In(y) + e2* -'=3y – 4x at the point…
A: Given that: lny + e2x-1 = 3y-4x We find slope of the tangent line at point (1/2,1) . Here i…
Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…
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Q: 1. Find the equation of the tangent line to x? + y? = 9, at the point (2, v5). %3D
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Q: What is the equation of the line tangent to the graph of y = 2x³/2 at the origin? Oy=0 Oy = 2r Oy =…
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Q: 3. Find the slope m of the tangent lines to the parabola y = -x+ 5x+ 6t its point of intersection…
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Q: 1. Find the equation of the lines tangent and normal to the curve 3x?y2=4x2-4xy. at the point…
A: Since you have asked multiple questions in single request so we will be answering only first…
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Q: find equation for the lines that are tangent andnormal to the curve at the given point. ex + y2 = 2,…
A: Given: Equation of curve ex+y2=2 and the point 0,1, To find: Equation of tangent and normal line to…
Q: Find for x? + x +y² + 2 = 3xy the lines that are tangent and normal to the curve at point (3,2).
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Q: Find the equation of the line that is tangent to the curve r = r In y, I> 0, at the point (1.e).
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Q: Find an equation of the tangent to the curve at the point (1, 81) I = e', y = (t– 9)2
A: Given: x=et,y=(t-9)2 at (1,81)
Q: Find the equation of a line tangential to the curve y = 2x² + 7x + 9 at P(1,18).
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Q: 10. Find the slope-intercept form of the equation of the line tangent to the graph of y arctan(9x)…
A: Given y = arc tan9xand x=39here we find the slope - intercept form of the equation of the line…
Q: At what point on the graph of f(x) = 3x² +x is the tangent parallel to the line with equation y = 4x…
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Q: d two coordinate points at which the tangent line to the curve given by x² – 2x + 4y² = 15 is…
A: if the tangent is vertical then dydx will be ∞x2-2x+4y2=15differentiate 2x-2+8ydydx=04ydydx=1-xsince…
Q: (b) Find the points on the curve y = 2x3 – 3x2 – 12x + 20 where the tangent is parallel to the…
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Q: What is the slope of the line tangent to the curve x2 + y2 = 1 and parallel to the x-axis ? OA…
A: what is the slope of the line tangent to the curve x2+y2=1 and parallel to the x axis
Q: 4. Consider the curve given by r³ + y³ = 9ry. Find the equation of the tangent line at (4,2).
A: To find the slope of the tangent we need dydx at (4,2)…
Q: Find the equation of the tangent line at the point (−2,2) to the curve defined implicitly below. 4y2…
A: We have to find tangent line to curve at given point at (-2,2).Cirve equation is given by:
Q: (b) Find the equation of the line normal to the tangent at the point x’y+xy² = 6.
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Q: (2) At what point(s) will the tangent line to y = x? - 4x +3 be horizontal
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Q: What is the slope of the tangent line that touches the graph of In y + e2a-1 = 3y – 4x at the point…
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Q: Find the equation of the tangent and length of the tangent to the curve y= x2+1 at (1,2)
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Q: 7. Find an equation of the line tangent to the curve y = 3x² – 1 and perpendicular to the line x
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Q: Given that x² + y? = (2x² + 2y² – x²)? Find an equation of tangent line to the curve at point (0,…
A: The formula to differentiate the product of two functions, f(x) and g(x) with a common variable is…
Q: Find an equation of the tangent line to the parabola y=x2 at the point P(1,1)
A: To find an equation of the tangent line to the parabola y=x2 at the point P1,1
Q: At what point is the tangent line to the curve y° = 6x² perpendicular to the line 2x – y – 1 = 0?…
A: Given: y3=6x2..(1)2x-y-1=0y=2x-1...2 As we know that, iI two lines are perpendicular to each other…
Q: Find an equation of the tangent to the curve at the given point. x 3 , y = t2 3, (3, 4)
A: Given curve is
Q: Find the equation of the tangent line to the curve y = 8 sin z at the point (, 4). 6
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Q: Find the equation of a line normal to the curve x^2=16y at (4,2).
A: Solve the given problem.
Q: Find the slope of the line tangent to y = 3x(cos x) at (7/2, 7/2). A) -3/2 B) 3x/2 C) /2 D) -x/2
A: Consider the function y=3x(cosx) Point : π2,π2
Q: Find a point on the graph where x = t² - 1, y = 2t has a vertical tangent.
A: For vertical tangents dx/dy=0
Q: Find an equation of the tangent line to the curve 2(2² + y?)? = 25(x² – y²) (a lemniscate) at the…
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Q: The slope of the tangent to the curve y²x + y²a² = 6 at (2, 1) is A B) -1 в 14
A: We can find the slope of the tangent to the curve at the indicated point as below.
Q: Find the slope and y-intercept of the tangent line, in the form y = mx + b, to the curve at the…
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Q: Find the slope of the tangent line to the curve (a lemniscate) 2(a² + y?)' = 25 (æ² – y²) at the…
A: The given equation of the curve: 2x2+y22=25x2-y2
Q: 1) Find the slope of the line tangent to the graph of y=x²+1at(2, 5).
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Q: What is the slope of the line tangent to the curve y = 3x² + 6x +3 at x = 4? Oy' = 51 O y' = 30 O y'…
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Q: find the equation of the line tangent to the curve y2+ exy=4 at point (0,2)
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Q: Find an equation of the line tangent to the curve y = v4x – 3 – 1 and perpendicular to the line x +…
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Q: For what value(s) of x is the line tangent to the curve y = xV6 - x horizontal? Vertical?
A: Given curve is: y=x6-x Differentiating with respect to x we get,…
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