Question

**13. Consider**

**f(x)=sqrt x-2**

**a) Using any of the three limit formulas to find f ′ ( a
), what is the slope of the tangent line to f ( x )at x = 18? (6
points execution, 2 points notation)**

**b) Find the equation of the tangent line at x =
18**

**14. State the derivative.**

**a) d/ d x [ x ^n ]**

**b) d /d x [ cos x ]**

**c) d /d x [ csc x ]**

**d) d/ d x [ cosh x ]**

**e) d/ d x [ ln x ]**

**f) d/ d x [ a x ]**

**g) d /d x [ sin ^− 1 x ]**

**h) d/dx [ tan^ − 1 x ]**

**15.Differentiate. Do not simplify.**

**f(x)=-4x^5+3/2x^3+x^⅔+10+7x^-2**

**16.Differentiate. Do not simplify.**

**g(x)=x^3secx**

**17. Differentiate. Do not simplify.**

**y=5sin (5x^2)+e^3x**

**18.Differentiate. Do not simplify.**

**k(x)= ln(tan x/3x)**

**19. Differentiate. Do not simplify.**

**n(t)=5t3^t cot t**

**20.Find the equation of the tangent line to the curve at
the point ( 0 , 2 ).**

** g(x)=e^x+1/x+1**

**21.Use implicit differentiation to find the slope of the
tangent line at**

**( π , π/ 2 ).**

**xsiny+2x-2y**

Answer #1

1. Differentiate the following functions. Do not simplify.
(a) f(x) = x^7 tan(x)
(b) g(x) = sin(x) / 5x + ex
(c) h(x) = (x^4 + 3x^2 - 6)^5
(d) i(x) = 4e^sin(9x)
(e) j(x) = ln(x) / x5
(f) k(x) = ln(cot(x))
(g) L(x) = 4 csc^-1 (x2)
(h) m(x) = sin(x) / cosh(x)
(i) n(x) = 2 tanh^-1 (x4 + 1)

1. Given f(x)=2x^3-3x^2+4x+2, find (f^(-1))'(14).
Differentiate and Simplify
2. f(x)=ln(3x) e^(-x^2 ) (Answer with positive exponents
Integrate and Simplify 3. ∫▒(6x^2-5x)/√x dx

Consider f(x) = x2 – 8x. Find its derivative using
the limit definition of the derivative. Simplify all
steps.
a. Find f(x + h).
____________
b. Find f(x + h) – f(x).
____________
c. Find [f(x + h) – f(x)] ÷ h.
____________
d. Find lim (hà0) [f(x + h) – f(x)] ÷ h.
____________
e. Find an equation of the line tangent to
the graph of y = x2 – 8x where x = -3. Present your
answer...

Let f(x, y) = x tan(xy^2) + ln(2y). Find the equation of the
tangent plane at (π, 1⁄2).

f(x) = 4x^2-5x+6
a) Find the slope in between where x=2 and x=3
b) Find the slope in between where x=3 and x=4
c) Find the slope in between where x=3 and x=a
d) Find the slope in between where x=3 and x=3+h
e) Use the answer in part c to find the slope of the line
tangent to f(x) at x=3
f) Use the answer in part d to find the slope of the line
tangent to f(x) at...

differentiate.
a. e^xtan(x)
b. sin(1/sqrtx)
c. ln(e^x/sqrt(x^2)+3)
d. subscriptx tan(x)
e. f(secx) where f'(x)= x/ln(x)

Differentiate the following fuctions.
(a) y=arcsin(e^x)
(b) f(x)=cosh x times 4^x
(c) y= ln ((x-1)^2/(3x+1))

1. Solve the equation ln(x + 5) − ln(x − 3) = 1 for x.
2.Find all values of x for which the following function has a
tangent line of slope 0 (i.e. f 0 (x) = 0). f(x) = e^2x+1 (2x +
5)
3.Calculate limx→−5 1 − √ x + 6/x + 5

1)If f(x)=2x-2 and g(x)=3x+9, find the following. a)
f(g(x))=? b) g(f(x))=? c) f(f(x))=?
2)Let f(x)=x^2 and g(x)=6x-16. Find the following: a)
f(3)+g(3)=? b) f(3)*g(3)=? c) f(g(3))=? d) g(f(3))=?
3) For g(x)=x^2+3x+4, find and simplify
g(3+h)-g(3)=?
Please break down in detail. Please and Thank
you

4)
Consider the polar curve r=e2theta
a) Find the parametric equations x = f(θ), y =
g(θ) for this curve.
b) Find the slope of the line tangent to this curve when
θ=π.
6)
a)Suppose r(t) = < cos(3t), sin(3t),4t
>.
Find the equation of the tangent line to r(t)
at the point (-1, 0, 4pi).
b) Find a vector orthogonal to the plane through the points P
(1, 1, 1), Q(2, 0, 3), and R(1, 1, 2) and the...

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