Find the parametrization of the tangent line to the space curve r(t) = (e" , sin(t), (t + 1)-³) at t = 0.

Q: Find all points on the curve o(t) = (t, t² - t + 3) where the tangent line passes through the origin

A: Yeah we will first find the equation of the tangent line for a general point (for t=a) then we will…

Q: Find the equation of the tangent plane to z = x² + 5y³ at (2, 1, 9).

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Q: Find the equation of the tangent plane to z = e* + y + y° +1 at the point (0, 4, 70).

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Q: Tom wants to invest $500. He invests in a company that predicts his investment will double in value…

A: Initial investment is $500 and the money gets doubled in 3 years.

Q: Let c(t) = (t^3 + 1, t^2 − 4t). Find:(a) An equation of the tangent line at t = 3

A: c(t)=t3+1 , t2-4t

Q: (5) Find the equation of the tangent plane to z = 1² + xy +3y* at r = 1, y = 1.

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Q: Find the slope of the tangent to the curvey=cos²x-sin'x at x- O a) 1 O b) 1/1/2 Oc) -2 d) 2

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Q: Given the function z = In(x - 2y), find the equation of the tangent plane when (x, y) = (3, 1) in…

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Q: Find the equation of the tangent plane to z = e² + y + y² +8 at the point (0, 4, 269). Z= 0

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Q: Determine the intersection point of the lines tangent to the curve r (t) = (senπt, 2senπt, cosπt) at…

A: The given curve is rt=sinπt,2sinπt,cosπt. Differentiating it with respect to t:…

Q: The population of a community is known to increase at a rate proportional to the number of people…

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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 the equation of the tangent plane to z= e" +x+x³ +1 the point (2, 0, 12).

A: Let a surface be represented by the function fx, y, z = c where c is a constant. Then the equation…

Q: Find the equation of the tangent plane to z = In(x³ + 1) + yª at the point (0,3, 81).

A: We have to find equation of tangent plane at (0,3,81).

Q: Find the tangent plane to the equation z = 5y cos(4x - 6y) at the point (6, 4, 20). z =

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