Use the given graphs to sketch the parametric curve x=f(t), y= g (t). x=f(t) y =g(t) 2 2 -1 2 -2 -1 t

Q: Find an equation of the tangent plane at the given point: (2,1) F(r.a) 3²-3,

A: Since you have posted a multiple question according to guidelines I will solve first question for…

Q: Find the points on the curve t² 16t+ 6, y X = = A. a horizontal tangent line B. a vertical tangent…

A: Given the curve is x=t2-16t+6  and y=t2+4t+3

Q: 6. Explain why the curve f(r) = r" + r* +x* + x +1 is always rising.

A: Given : f(x) = x7+ x5 + x3 + x + 1  To find : Explain why f(x) is always rising or increasing.…

Q: The parabola y = x2 + C is to be tangent to the line y = x. Find C.

A: To find the value of C.

Q: 3. Sketch the curve: y = (x²–1)(x+2) x-3

A: y=(x2-1)(x+2)(x-3)y=(x-1)(x+1)(x+2)(x-3)X-intercept:(-2, 0), (-1, 0), (1, 0)Y-intercept:(0, 23)…

Q: Find the length (in units) of the curve y =    16 − x2between x = 0 and x = 2.

A:

Q: graphically represent the curve described by the following functions f(t) = (t, V4 – t2)

A: Any point in the cartesian coordinate system is defined as x,y . The parametric functions are…

Q: Therefore, the curve y = x* - 2x2 + 2 has horizontal tangents at x-0, 1, and -1

A: Just compute the derivative and equate it to zero.

Q: (ii) Find the length of the curve y = E* from x = 0 to x = 2. %3D

A:

Q: Sketch the two curves 7(t) = tî + t²j; t e [1, 5] and B(T) = e"î + e²r3; T E [0, In 5]. How are they…

A:

Q: What is the slope at t = −2 ?

A:

Q: A mouse Q runs along the positive y-axis at the constant speed v at the origin. A cat P chases the…

A: It is given that∙Mouse Q runs along y-axis with a constant velocity v1∙Cat P runs along curve C with…

Q: (2) Find all points on the graph y = x3 - 12x + 9 with horizontal tangents. Find dy d2y and dc d2…

A: Given:

Q: Determine the stationary point of the curve y=x-In(1+x).

A:

Q: Find the Cartesian equation of the curve defined by the following parametric equations . after…

A:

Q: Find the points on the curve z t? – 10t – 8, y = t² + 4t + 6 that have: A. a horizontal tangent line…

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you.  If…

Q: If f (−θ) = f (θ), then the curve r = f (θ) is symmetric with respect to the (choose the correct…

A: