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
