25,270 Answered Questions for the topic calculus

Calculus Precalculus

06/12/24

Law of Logarithms 4.4 (1)
The logarithm of a product of two numbers is the same as the sum  of the logarithms of these numbers. So log4(16 · 64) = log4(16) +  __________
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Calculus Precalculus

06/12/24

4.4 Laws of Logarithms (3)
The logarithm of a number raised to a power is the same as the  times the logarithm of the number. So log4(1614) = 14 ·__________
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Calculus Precalculus

06/12/24

4.4 (11) laws of logarithms
Use the Laws of Logarithms to combine the expression.(1/2)log2(6) − 2 log2(7)
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Calculus Precalculus

06/12/24

4.3 (1) logarithmic functions

The function f(x) = log16(x) is the logarithm function with base ____________. So f(16) =  __________, f(1)=_____________, f(1/16)____________, f(25)=_____________, and f(4)___________.
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Calculus Math Trigonometry

06/11/24

Maximum of a Trigonometric Function (Calculus)
For the function h(t)=e-tsin(t), state the first maximum and when it occurs.
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Calculus

06/11/24

calculus area question
Estimate the area under the graph of the function f(x)=x+2−−−−−√ from x=−1 to x=3 using a Riemann sum with n=10 subintervals and midpoints. Round your answer to four decimal places. area =
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Calculus

06/11/24

Cross Product‎ ‎ ‎

Given u times v = <2,1,4> find (u-2v)times(u+4v)
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Calculus Math Trigonometry

06/11/24

Derivatives of Trigonometric Functions (Equation of a Tangent Line)
Find the equation of the line tangent to f(x)=2sin(x)cos(x) at x=5π/18. Round your slope and y-intercept to 2 decimal places.(I've got the derivative figured out: f'(x)=-2sin2(x)+2cos2(x), but I... more
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Calculus Math Trigonometry

06/11/24

Derivatives of Trigonometric Functions Help
The voltage of a power supply is given by the equation V(t)=100sin(4πt)+40. State the maximum voltage and the times when it occurs.(I'm fairly confident that I have the derivative correct:... more
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Calculus Precalculus

06/10/24

3.6 (1) --- Rational Functions

If the rational function y = r(x)  has the vertical asymptote x = 1, then as x → 1+,  eitherY-->________ (smaller value)Y-->________ (larger value)
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Calculus

06/08/24

Calculus Special Trig Limits
I'm stuck on this problem: Lim x approaching 0 (Sec(x) - 1) / (sin(x)
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Calculus

06/06/24

Find the volume of the resulting solid,
if the region under the curve y = 5/(x2 + 3x + 2) from x = 0 to x = 1 is rotated about the x-axis and the y-axis. x-axis? y-axis? I tried solving for the rotation about the x-axis and I got ∫(from... more
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Calculus

06/06/24

Related Rates Triangular Prism
A trough is 12 feet long and 3 feet across the top. Its ends are isosceles triangles with altitudes of 3 feet.(a) If water is being pumped into the trough at 2 cubic feet per minute, how fast is... more
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Calculus

06/05/24

Write out the form of the partial fraction decomposition of the function. Do not determine the numerical value the coefficient.
(x^2/(x^2+x-56)) = I tried solving this question by dividing the numerator by the denominator and I got 1+ (56-x/(x^2+x-56). I simplified the denominator and I got 1+(56-x/(x+8)(x-7) ). Lastly, I... more
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Calculus

06/04/24

Calc 1 - related rates problem
A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. Find the rate (rad/sec) at which the angle between... more
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Calculus

06/04/24

Average Velocity
Problem: h(t) = -16t^2 + 96t + 100, what is the average velocity between t = 4 and t = 5. Find the equation of the secant line between (4, h(4) and (5, h(5).What I did: [-16(5)^2 + 96(5) + 100] -... more
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Calculus Precalculus

06/04/24

3.3, (13) Consider the following

P(x) = x3 + 2x2 − 9x − 18,    c = −2Show that the given value of c is a zero... more
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06/03/24

3.1 6, a quadratic function is given
A quadratic function f is given.f(x) = −4x2 − 20x + 4(a)Express f in vertex form.(b) Find the vertex and x- and y-intercepts of f. (If an answer does not exist, enter DNE.)vertex:X intercept... more
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Calculus Precalculus

06/03/24

3.1 5, a quadratic function is given
A quadratic function f is given.f(x) = −x2 + 16x(a)Express f in vertex form.f(x) =   (b)Find the vertex and  x- and y-intercepts of f. (If an answer does not exist, enter DNE.)vertex(x, y)vertex:X... more
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Calculus Precalculus

06/03/24

A quadratic function f is given. 3.1 (4)
f(x) = x2 + 6x − 5a. express f in standard form (b) Find the vertex and  x- and y-intercepts of f. (If an answer does not exist, write N/A) Vertex (x,y):___________ x- Intercepts (x,y)_________... more
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Calculus Precalculus

06/03/24

The quadratic function f(x) = a(x − h)2 + k is in vertex form.
The quadratic function f(x) = a(x − h)2 + k is in vertex form. The graph of f is a parabola with vertex (x, y) = __________   3.1 (2)
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Calculus Precalculus

06/03/24

Factor the Polynomial using factored form 3.2 (13)

Factor the polynomial and use the factored form to find the zeros. (Enter your answers as a comma-separated list. Enter all answers using the appropriate multiplicities.)P(x) = x4 − 8x2 − 9X=______?
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06/03/24

3.2 Polynomial functions and their graphs (15)
The graph of a polynomial function is given.P(x)= -(1/2)x^3 + (3/2)x - 1 The x y-coordinate plane is given. The curve enters the window in the second quadrant, goes down and right becoming less... more
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Calculus

06/03/24

Show 2nd derivatives with respect to x of both y=(1-x^2)^(1/2) and y=-(1-x^2)^(1/2) are not zero at x=1
for x2+y2=1 show 2nd derivatives with respect to x for both semicircle functions do not exist at x=1 and x=-1.
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06/03/24

In interval notation (17) 3.2 Polynomial functions
A cardboard box has a square base, with each edge of the base having length x inches, as shown in the following figure. The total length of all 12 edges of the box is 144 in.A box with a square... more
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