Calculus 1 Exam 2

domain and range of y=logx

domain (0,∞) range (-∞,∞)

domain and range y=lnx

domain (0,∞) range(-∞,∞)

domain and range y=a^x

domain a>0 range a>1 a≠1

What are the domain and range of f? f(x)=lnx+7 what is the x-intercept of the graph of f?

domain= (0,∞) range=(-∞,∞) x=1/e^7

Let y=tanx Evaluate dy and ∆y if x=π/3 and dx=-0.2( Round ∆y to four decimal places)

dy= -0.8 ∆y--0.6001

Find the differential of each function y=tan √7t

dy=7sec²√7t/2√7t(dt)

Let y=tanx Find the differential dy

dy=sec²(x)dx

Differentiate the function f(x)=log11(xe^x)

f¹(x)=1+x/xln(11)

Express the given quantity as a single logarithm 1/9ln(x+2)⁹+1/2[lnx-lnx(x²+3x+2)²]

ln(x^(1/2)/x+1

g(x)=cosx determine whether it is one-to-one

no

domain and range of y=e^x

range (0,∞) domain(-∞,∞)

ysin(x)=xsin(y²)

sin(y²)-2xycos(x²)/sin(x²)-2xycos(y²)

solve for x e^3x+1=p

x=(ln(p)-1)/3

solve for x log₃(nx)=a

x=3^a/n

Use implicit differentiation to find an equaion of the tangent line to the curve at the given point. y²(y²-4)=x²(x²-5) (0,-2) (devil's curve)

y=-2

g(x)= 2/x Determine whether it is one-to-one.

yes

Differentiate y= ln(5x²+3y²)

y¹=10x/5x²+3y²-6y

Find the derivative of the function y=4^{5x^2}

y¹=4^{5x^2}(ln(4)5{x^2}(ln(5))(2x))

Differentiate the function y=√2+2e^9x

y¹=9e^9x/√2+2e^9x

Differentiate the function y=tan[ln(ax+b)]

y¹=asec²[ln(ax+b)]/ax+b

Use logarithmic differentiation y=√x-2/x⁴+1

(-3x⁴+8x³+1)/2√x-2(x⁴+1)^(3/2)

f(x)=64-e^{x^2}/1-e^{64-x^2}what is the domain

(-∞,-8)u(-8,8)u(8,∞)

find the domain of g(t)=√1-5^t

(-∞,0]

domain of f(x)=a^x

(-∞,∞)

find domain of f()=sin(e^-t)

(-∞,∞)

find domain of f(x)= 4+x/e^{cosx}

(-∞,∞)

Solve inequality for x lnx<0

(0,1)

if a≠1, what is the range of this function

(0,∞)

Find the derivative y=ln(3x)/x^6

(1-6ln((3x))/x^7

Differentiate the function. y = e^ktan√7x

(7ksec²(√7x)/2√7x )×e^ktan√7x

tan(x-y)=y/8+x²

(8+x²)sex²(x-y)+2xtan(x-y)/1+(8+x²)sec²(x-y)

Find the differential y=ucosu

(cos(u)-usin(u))du

Find (f^-1)¹(a) f(x)=3x³+3x²+8x+4 a=4

(f^-1)¹(a)=1/8

solve inequality or x e^x>4

(ln(4),∞)

Find the second derivative

-(-42ln(3x)+13)/x^8

If f(x) +x²[f(x)]⁴=18 and f(1)=2, find f¹(x)

-32/33

Find y² by implicit differentiation 5x³+2y³=1

-5x/2y⁵

Find the differential of each function y=2-v²/2+v²

-8v/(2+v²)²(dv)

lim x→4+ ln(x²-16)

-∞

find the limit lim x→∞ (e^(-8x)cosx)

0

lim x→∞ (7π/2)+ e^tanx

0

Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05 cm thick to a hemispherical dome with diameter 42 m. (Round your answer to two decimal places.)

1.39 m³

Find (f^-1)¹(a) a=2 3x³+2sinx+2cosx

1/2

find a formula for the inverse of the function f(x)= 2 + √4+6x

1/6(x-2)²-2/3

8x²+7xy-y²=4

16x+7y/2y-7x

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x²+2xy-y²+x=20 (4,8)

25/8x-9/2

f(x)=x/1-ln(x-8) Differentiate f and find the domain f(x)=x/1-ln(x-8)

2x-ln(x-8)(x-8)-8/(x-8)(1-ln(x-8)² domain=(8, e+8)u(e+8,∞)

Use a linear approximation to estimate the given number (1.999)⁵

31.92

Use a linear approximation to estimate the given number (8.06)^(2/3)

4.02

Find the differential y=s/(6+5s)

6/(6+5s)²(ds)

Find an equation of the tangent line to the curve at the given point. y = ln(x^2− 7x + 1), (7, 0)

7x-49

Find the linearization L(x) of the function at a f(x)=x^(1/2) a=16

L(x)= 2 +1/8x