Find an equation of the line tangent to the curve at the point corresponding to the given value of t. 57 x= cos t+tsint, y = sint-t cos t; t= 4 (Type an equation. Simplify your answer. Type your answer in slope-intercept form. Type an exact .

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A: We will first find the slope of the line

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A: Let (?/6 , 1) =(x1 , y1)  Using the slope - intercept formula : ( y - y1) = m( x - x1 ) or y =mx +b

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A: Topic - equation of tangent line to curve at given point

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A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: the equation of the tangent line to the curve y = 4 sin x at the point equation of this tangent line…

A: We are asked to find the tangent line of the curve.

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A: For t=1,x=1+11=1+1=2y=1-11=0

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A: The solution is given as follows

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A: Given:y=sin-1x6  at 3,π6Tangent line:y-y1=mx-x1m=dydx

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A: we have to follow steps

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A: Differentiate at given point and for and slope then use equation of tangent line

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A: This question is based on straight line. The general equation of a straight line is            y =…

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A: Given equations - x = sec2t-1                                       x = tan2t         .........(1)…

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A: We know that the expression for slope of tangent to the curve at a point P(x, y) is: m=dydxp(x,y)…

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Q: (a) Find an equation of the tangent line to the curve y = 12x sin(x) at the point (T/2, 67).

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A: Equation relates the number of variables combined together by algebraic entities using equality…

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A: Given data is: x=sint , y=csct  and t=-π6

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A: Given query is to find the equation of tangent line. Since slope of  tangent is given by derivative…

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Q: 7. x = sec t, y = tan t, t = T/6

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A: We have to solve the problem

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A: We are asked find the equation of the curve.

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A: Given: y=4sin x point (π6, 2)

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A: given function :

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A: The given curve is: y2=x3(7-x)

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A: The given graph and the point is

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A: The explanation of answer as follows :-

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A: Given, x3+3xy2+y3=1

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Q: 4. Consider the curve defined by 2x2 - cot(y) = 5. Which of the following is an expression for the…

A: 2x2-coty=5 2x2-coty-5=0 to find the slope, we need to take the derivative ddx2x2-coty-5=0

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A: This question is related to equation of straight line, we will solve it using given information.

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