2. Which of the following functions grow faster than e as x–→∞? Which grow at the same rate as e"? Which grow slower? a. 10x4 + 30x + 1 c. Vi + x* b. x In x — х d. (5/2)* f. хе e. e¯* h. e*-1 g. ecos x х

Q: - { S 1² – 3 if r -1 2. Determine the constant k such that the function f(r) is continuous at r =…

A:

Q: Is there a sequence of continuously differentiable functions: fn : R –→ R such that fn → x and f. →0…

A: Yes, the sequence is given in step 2.

Q: - Which of the following functions grow faster than In x as x→ o0o? Which grow at the same rate as…

A: Derivative of a function determines the change of variable with respect to another variable. Whereas…

Q: if two resistors with resistances R1 and R2 are connected parallel, then the total Resistance R…

A: Given,

Q: 4. Recall that (in z) = ±(=) =é, and that (a*) = e* In a, where a>0 is a constant (as deduced in…

A:

Q: Suppose that z =x*y°,where bothx and y are changing with time. At a certain instant when x = 1 and y…

A: Derivative formula ddxxn= n xn-1Product ruleuv'=u'v+uv'

Q: Suppose that z = x*y°, where both x and y are changing with time. At a certain instant when x = 1…

A: For the solution of the problem follow the next step.

Q: Suppose F 1  and F 2 are both antiderivatives of f on an interval I How are  F 1  and F 2  related?

A: Given:  F 1  and F 2 are both antiderivatives of f on an interval I. That is,

Q: Find the absolution extrema of f(x) = (In x)2 on [1, e].

A: We have to determine absolute extrema of girls question

Q: Determine the value of the arbitrary constant of the antriderivative of F(x) = x-In(x) given the…

A:

Q: Given the function f(x) = 3x/3, which of the following is a valid formula for the instantaneous rate…

A: Recall: Instantaneous rate of change of f at x=a :          limh→0f(a+h)-f(a)h

Q: Suppose that z = x³y², where both x and y are changing with time. At a certain instant when x = 2…

A:

Q: Differentiate the function with respect to the independer X f(x) = +e5x + e 2 e (x) = 0

A:

Q: 4. Which of the following functions grows at the same rate as 3^ as x g O 2x O√√3x +4 3* O √6x 0x +…

A: To compare the rate of growth between the given functions lets draw their graphs. Given function 3x,…

Q: 4. Which of the following functions grows at the same rate as ex as x goes to infinity? ex+3 e3x e2x…

A: We find which of the following functions grow at the same rate as ex as x goes to infinity: (1) ex+3…

Q: |81. Recall that the present value (PV) of an investment that pays out income continuously at a rate…

A: The present value (PV) of an investment that pays out income continuously at a rate R(t) for T years…

Q: (4) Consider the graph of f(x) = Vr below. Is f(x) differentiable at r = 0? If so, what is f'(0) and…

A: Given function is fx=x3

Q: nestion 6 Researchers have observed that the daily energy requirements of female Collies who are at…

A: Here we will find the total energy required for female collie between her second and fourth birthday…

Q: Lemons are harvested from a certain orchard at a rate modeled by L(t)= 20t - t^2 bushels per hour…

A: The rate is given by the function L(t) = 20t -t2, and the values of t vary between 0 to 10. The…

Q: Suppose that h = 2x'y, where both x and y are changing with time. At a certain instant when x = 1…

A:

Q: Suppose that z = x²y³, where both x and y are changing with time. At a certain instant when x = 2…

A:

Q: If two resistors with resistance R1 and R2 are connected in parallel, the total resistance R in ohms…

A:

Q: 8. Let n(t) represents the rate of growth of a population of grizzly bears at time t (in years).…

A:

Q: 4. Find the maximum value of f (x) = In(x – In x) on the interval -sse. e

A:

Q: Suppose that z = x²y°, where both x and y are changing with time. At a certain instant when x = 2…

A: Explanation of the answer is as follows

Q: 3. Find the value of k that will make f continuous on (-o, 00). NORS x + 19 if x 1

A:

Q: Compute the Toylor serias about x= o of the function orcton (at -) up to t# terms of dlearee thre.…

A:

Q: 10. Estimate the instantaneous rate of change of f(x) = interval with h= 0.001. Round to 2 decimal…

A: Let us find the instantaneous rate of change of the given function in the next step.

Q: b) Sand is leaking from a bag in such a way that after t seconds, there are S(t) = 50 (1 –9 * pounds…

A: Given:-Snad is leaking from a bag after t second isS(t) = 501 - t2153(a) Put t = 0 to find…

Q: 3. Suppose that {f(t)} = F(s) with F a differentiable function and that L{f'(t)} Exists. Then…

A:

Q: If f(x) = SEs rlog3 x 3t %3D dt and is differentiable on an interval, which cotx csc2t of the ff. is…

A:

Q: 4. If two resistors with resistance R1 and R2 are connected in parallel, the total resistance R in…

A:

Q: Find the linearizationsof the following functions at x = 0. ln (1 + x)

A:

Q: Suppose h (x) =() . What is the correct result of the derivative of h with respect to x? ". In (5) A…

A: Derivative using chain rule of differentiation.

Q: Suppose that z = x³y²2, where both x and y are changing with time. At a certain instant when x = 1…

A: The product rule of differentiation states that ddtfg=fdgdt+gdfdt. The power rule of differentiation…

Q: (a) The sales of a book publication are expected to grow according to the function S = 300000(1 –…

A: a)). To calculate maxima dSdt=0.Thus:dSdt=0ddt(300000(1-e-0.06t))=0e-0.06t=0=0t→∞

Q: (a) The sales of a book publication are expected to grow according to the function S = 300000(1 − e…

A:

Q: 4. Recall that (In z) = 1, £(") = e", and that £(a") = a" In a, where a > 0 is a constant (as…

A:

Q: 1. Which is correct? Over the period [16, 20] the instantaneous rate of change of N is: (A)…

A: Since you have asked multiple questions, therefore I will solve first 3 questions for you. If you…

Q: Suppose g: IR →IR is a differentiable functionN with bounded derivative, Fix e> 0 , and defive fix)…

A: Consider the given information.

Q: (2) Assume that we have a Cobb-Douglas production function for a certain industry: Q = CL°K®, where…

A:

Q: A radioactive matierial decays according to the function A0e-0.0244t where A0 is the intial amount…

A:

Q: h(x) = (5x-1 d) m(x) = (4x² – 9x} %3D

A: Product rule of differentiation: u·v' = u·v' + v·u'   ddxxn = n·xn-1 ddxf(x)n = n·f(x)n-1·f'(x)

Q: 7. If the number of bees in a beehive are modeled by the function 6(t) = te +1 thousand bees, where…

A: The number of bees in a beehive modeled by b(t)=te-t210+1 thousand bees,where t is in months past…

Q: Suppose that z = x'y, where both x and y are changing with time. At a certain instant when x = 1 and…

A: z=x3y2 and  x is decreasing at the rate of 2 units/s y is increasing at the rate of 3 units/s We…

Q: Q2/ A tank contains initially (150) liter of brine in which (60)N of salt is dissolved starting at…

A: The amount of salt in the tank at the end of 5 min is 111.38779 N

Q: 7. If the number of bees in a beehive are modeled by the function b(t) = te +1 thousand bees, where…

A:

Q: 4. Recall that (in z) = £e) ==, and that (a") = a* In a, where a >0 is a constant (as deduced in…

A: Here we use chain rule of differentiation. f(x)= g(h(x)). f'(x)=g'(h(x)).h'(x).