1. Find the equation of the lines tangent and normal to the curve 3x?y?=4x2-4xy at thepoint (1.-2).2. Find the slope of the tangent line to the curve x²+y?=1 at the point )dy3. For each problem finddx5x3+xy? = 5x³y³а.b.x²y+3xy³-x = 3y= e*sin2x+x?с.d.y= x?Inx?Find the absolute maximum and absolute minimum values of f on the given interval4.and state where those values occur:f(x)=x³-3x2-9x+25, [-5,10]www5.For f (x) = -x3-3x²+45x-5 find the following:f(x)а.b.the critical pointsthe interval(s) where the function is increasingс.d.the interval(s) where the function is decreasing 6.During one study of red squirrels the number in one area was modeled by thefunction N(x) = x3 – 11x? + 39x- 47, 1

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Answered: 1. Find the equation of the lines…

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Calculus

1. Find the equation of the lines tangent and normal to the curve 3x?y2=4x2-4xy. at the point (1,-2).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 94E

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Question

100%

1. Find the equation of the lines tangent and normal to the curve 3x?y?=4x2-4xy at the
point (1.-2).
2. Find the slope of the tangent line to the curve x²+y?=1 at the point )
dy
3. For each problem find
dx
5x3+xy? = 5x³y³
а.
b.
x²y+3xy³-x = 3
y= e*sin2x+x?
с.
d.
y= x?Inx?
Find the absolute maximum and absolute minimum values of f on the given interval
4.
and state where those values occur:f(x)=x³-3x2-9x+25, [-5,10]
www
5.
For f (x) = -x3-3x²+45x-5 find the following:
f(x)
а.
b.
the critical points
the interval(s) where the function is increasing
с.
d.
the interval(s) where the function is decreasing

6.
During one study of red squirrels the number in one area was modeled by the
function N(x) = x3 – 11x? + 39x- 47, 1<x< 12 Where x is the number of years since the
study started. During what years was this a decreasing function?
7.
Evaluate the following integrals:
dx
1 Vxa+9
а.
S 5xcos(x?) dx
S sin52xcos2xdx
b.
C.
d.
Sx³e*dx
8.
Find the area enclosed by the curve y=x2-2x and the x axis from x=0 to x=3.

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