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study help
mathematics
calculus early transcendentals 9th
Questions and Answers of
Calculus Early Transcendentals 9th
Radiocarbon Dating Scientists can determine the age of ancient objects by the method of radiocarbon dating. The bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive
Calculate y'. e y = .2
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.The derivative of a rational function is a
Differentiate.f (θ) = sin θ/1 + cos θ
Prove the identity.cosh x + sinh x = ex
Differentiate the function.s(t) = 1/t + 1/t2
Find the derivative of the function.F(t) = (1/2t + 1)4
Find dy/dϰ by implicit differentiation.eϰ sin y = ϰ + y
Differentiate the function.p(t) = ln √t2 + 1
Differentiate.G(u) = 6u4 – 5u/u+1
Radiocarbon Dating Scientists can determine the age of ancient objects by the method of radiocarbon dating. The bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive
Find the differential of the function.y = √1 – t4
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f(x) = (x6 – x4)5, then f(31)(x) = 0.
Differentiate.f (ϰ) = eϰ sin ϰ + cos ϰ
Prove the identity.cosh(− x) = cosh x(This shows that cosh is an even function.)
Differentiate the function.V(t) = t–3/5 + t4
Find the derivative of the function.g(t) = 1/(2t + 1)2
Find dy/dϰ by implicit differentiation.sin ϰ + cos y = 2ϰ – 3y
Differentiate.g(t) = 3 – 2t/5t + 1
Radiocarbon Dating Scientists can determine the age of ancient objects by the method of radiocarbon dating. The bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive
Calculate y'.y = √x cos √x
Find the differential of the function.y = e5ϰ
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.The derivative of a polynomial is a
The weight w of an astronaut (in pounds) is related to her height h above the surface of the earth (in miles) bywhere w0 is the weight of the astronaut on the surface of the earth. If the astronaut
Differentiate.H(t) = cos2t
Prove the identity.sinh(−x) = −sinh x(This shows that sinh is an odd function.)
Differentiate the function.f (ϰ) = ϰ3/2 + ϰ–3
Find the derivative of the function.f (ϰ) = 1/3√ϰ2 – 1
A sample of einsteinium-252 decayed to 64.3% of its original mass after 300 days.(a) What is the half-life of einsteinium-252?(b) How long would it take the sample to decay to one-third of its
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. d -1x² +x| = |2x + 1| dx
Verify the given linear approximation at a = 0. Then determine the values of ϰ for which the linear approximation is accurate to within 0.1.2/1 + eϰ ≈ 1 – 1/2ϰ
Differentiate.g(θ) = eθ(tan θ – θ)
Write cosh(4 ln x) as a rational function of x .
Differentiate the function.r(z) = z–5 – z1/2
Differentiate.y = eϰ/1 – eϰ
Find the derivative of the function.f (ϰ) = √5ϰ + 1
Differentiate the function.g(ϰ) = ln(xe–2ϰ)
The half-life of cesium-137 is 30 years. Suppose we have a 100-mg sample.(a) Find the mass that remains after t years.(b) How much of the sample remains after 100 years?(c) After how long will only 1
Differentiate.y = ϰ ⁄eϰ
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. d (tan?x) dx d (sec?x) dx
Suppose 4ϰ2 + 9y2 = 25, where ϰ and y are functions of t.(a) If dy/dt = 1/3, find dϰ/dt when ϰ = 2 and y = 1.(b) If dϰ/dt = 3, find dy/dt when ϰ = –2 and y = 1.
Differentiate.f (θ) = (θ – cos θ) sin θ
Write sinh(ln x) as a rational function of x.
Differentiate the function.W(v) = 1.8v–3
Find the derivative of the function.f (ϰ) = (ϰ5 + 3ϰ2 – ϰ)50
Differentiate the function.y = 1/ln ϰ
Strontium-90 has a half-life of 28 days.(a) A sample has initial mass 50 mg. Find a formula for the mass remaining after t days.(b) Find the mass remaining after 40 days.(c) How long does it take the
Differentiate.g(ϰ) = (ϰ + 2√ϰ ) eϰ
Calculate y'.xey = y sin x
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. d (In 10) dx 10
Differentiate.y = sin θ cos θ
Write 2e2x + 3e−2x in terms of sinh 2x and cosh 2x.
Differentiate the function.F(t) = t3 + e3
Find the derivative of the function.f (ϰ) = (2ϰ3 – 5ϰ2 + 4)5
Suppose that the graph of the velocity function of a particle is as shown in the figure, where t is measured in seconds. When is the particle traveling forward (in the positive direction)? When is it
Differentiate the function.f(ϰ) = ln 1/ϰ
Differentiate.f (x) = (3ϰ2 – 5ϰ)eϰ
Calculate y'. t4 – 1 y 14 + 1 - 1
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. d (10*) = x10*-1 dx
Verify the given linear approximation at a = 0. Then determine the values of ϰ for which the linear approximation is accurate to within 0.1.tan–1ϰ ≈ ϰ
Show that sin-1(tanh x) = tan-1(sinh x).
Write 8 sinh x + 5 cosh x in terms of ex and e−x.
Differentiate the function.f (t) = –2et
Write the composite function in the form f (g(ϰ). [Identify the inner function u = g(ϰ) and the outer function y = f(u).] Then find the derivative dy/dϰ.y = 3√eϰ + 1
Graphs of the position functions of two particles are shown, where t is measured in seconds. When is the velocity of each particle positive? When is it negative? When is each particle speeding up?
Differentiate the function.f(ϰ) = ln(sin2 ϰ)
The table gives census data for the population of Indonesia, in millions, during the second half of the 20th century.(a) Assuming the population grows at a rate proportional to its size, use the
Differentiate.y = (eϰ + 2)(2eϰ – 1)
Calculate y'.y = x cos-1x
Differentiate.g(ϰ) = 3ϰ + ϰ2 cos ϰ
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If y = e2, then y' = 2e.
Find the numerical value of each expression.(a) sinh 1(b) sinh-1 1
Differentiate the function.g(ϰ) = 7/4 ϰ2 – 3ϰ + 12
Write the composite function in the form f (g(ϰ). [Identify the inner function u = g(ϰ) and the outer function y = f(u).] Then find the derivative dy/dϰ.y = e√ϰ
Differentiate.y = ϰ3 eϰ
Calculate y'.y = x2 sin πx
Differentiate.h(θ) = θ2 sin θ
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f is differentiable, then d de (Vx) =
Give several examples of how the derivative can be interpreted as a rate of change in physics, chemistry, biology, economics, or other sciences.
Iffind the value of f'(π/4). sec t - lim sec x f(x) t - x
Find the numerical value of each expression.(a) sech 0(b) cosh-1 1
Differentiate the function.f (ϰ) = ϰ75 – ϰ + 3
Write the composite function in the form f (g(ϰ). [Identify the inner function u = g(ϰ) and the outer function y = f(u).] Then find the derivative dy/dϰ.y = tan(ϰ2)
A particle moves according to a law of motion s = f (t), t ≥ 0, where t is measured in seconds and s in feet.(a) Find the velocity at time t.(b) What is the velocity after 1 second?(c) When is the
Differentiate the function.g(ϰ) = 4ϰ + 7
Differentiate.y = (10ϰ2 + 7ϰ – 2)(2 – ϰ2)
Calculate y'. tan x y : 1 + cos x
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f is differentiable, then f'(x) d VF(x) dx
Find the linearization L(ϰ) of the function at a.f (ϰ) = cos 2ϰ, a = π/6
Find the numerical value of each expression.(a) sinh 4(b) sinh(ln 4)
Write the composite function in the form f (g(ϰ). [Identify the inner function u = g(ϰ) and the outer function y = f(u).] Then find the derivative dy/dϰ.y = sin(cos ϰ)
A particle moves according to a law of motion s = f (t), t ≥ 0, where t is measured in seconds and s in feet.(a) Find the velocity at time t.(b) What is the velocity after 1 second?(c) When is the
Differentiate the function.f(ϰ) = ln(ϰ2 + 3ϰ + 5)
A culture of the bacterium Salmonella enteritidis initially contains 50 cells. When introduced into a nutrient broth, the culture grows at a rate proportional to its size. After 1.5 hours the
Differentiate.y = (4ϰ2 + 3)(2ϰ + 5)
Calculate y'. x² y = — х + 2
Differentiate.y = ϰ2 + cot ϰ
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f and g are differentiable, then d
Find the linearization L(ϰ) of the function at a.f (ϰ) = 3√ϰ , a = 8
Find the numerical value of each expression.(a) cosh(ln 5)(b) cosh 5
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