Question

y=x^3-2x^2+3x-1

what is the gradient of the normal line at x =-3

answer correct to 3 decimal places

Answer #1

find y' for the function
1. (y-2)^7=3x^2+2x-2
2. 3y^3+2x^3=3
3.(4y^2+3)^4+3x^5-5=0
4. 4x^2+3x^2y^2-y^3=3x

Find the area of the indicated region.
between y=2x^2+6x-3 and y=-x^2+3x+3 for x in [-2,2]

solve the system of equations
1: y=3x^2-2x-1
2x+3y=2
2: x^2+(y-2)^2=4
x^2-2y=0

find the area of the region bounded by the graph of
y=x^3-2x^2-x+2 and y=3x^2-5x+2

f(x)=3x^4-7x^2+2x+1
Find the tangent line at x=2

(3)If H(x, y) = x^2 y^4 + x^4 y^2 + 3x^2 y^2 + 1, show that H(x,
y) ≥ 0 for all (x, y). Hint: find the minimum value of H.
(4) Let f(x, y) = (y − x^2 ) (y − 2x^2 ). Show that the origin
is a critical point for f which is a saddle point, even though on
any line through the origin, f has a local minimum at (0, 0)

Solve using Gaussian Elimination with back subsitution:
3x(1) - 2x(2) + x(3) =3
2x(1) + 4x(2) - 2x(3) = 2
4x(1) - 2x(2) - 3x(2) = -12

what is the area between the curves y=x^3+x^2-1 and
y=2x^2+2x-1

Find the line intersection and the angle between the planes
3x-2y+z=1 and 2x+y-3z=3.

1-solve for x and y
3x+(y-2)i=(5-2x)+(3y-8)i
2-solve for z and write the answer with standard form
(3-2i)z+(4i+6)=8i
3-preform the indicated operation and write the answer with
standard form
(9+5i)-(6+2i)

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