Given the function f(x) = 3x/3, which of the following is a valid formula for the instantaneous rate of change at I = 343? Select the correct answer below: 21 – 3h/3 lim h-0 3(343+h)/3- 21 O lim h0 3h/3 + 21 lim h-→0 3(343+h)/3- 3h/3 O lim h-0

Q: Find the limit, if it exists. V(t + 25)(t – 1)² lim 11t - 11 t-1+

A:

Q: Find the derivative of the composite natural exponential functions 1. f(x) = In( 2. g(x) = In(v³ +1)…

A:

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: 4. Suppose f(x) = -3x+ log2x and g(x) = 2*. Find the AROC (average rate of change) of the composite…

A: Given the function is fx=-3x+log2xgx=2x

Q: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

A: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

Q: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

A: Given that the function f(x) = | x - 1|

Q: Suppose that copper is being projected to be extracted from a certain mine at a rate given by P'(t)…

A: (a)

Q: Find the equation of the secant line for f(x) = log2 (3x² + 2x – 1) from x = 1 to x = 3.

A:

Q: 2. Suppose that a model rocket blasts off, straight up, at time t = 0, with a vertical displacement…

A: If f(t) represent displacement of rocket  then f'(t) represent velocity and f''(t) represents…

Q: What is the closest value to the instantaneous rate of change of the following function at x = 2?…

A: Instantaneous rate of change of a function at a point represented by the slope of the line at that…

Q: A recent report by the U.S. Cen- sus Bureau predicts that the U.S. Hispanic population will increase…

A:

Q: 1. Evaluate. a) lim x--2 ³-2x² +12 x² +1 x² -8x+7 b) lim x-7 2. What is the average rate of change…

A:

Q: Q1: Find the derivative of the functions. 5- y = (csche)(1- In csche) 6- y = log3 (1 + 0 In 3) %3D

A: 5. y=cschθ1-ln cschθ6. y=log31+θ ln3

Q: Given the graph of derivative f'(x), find: a) Any interval(s) where f(x) is decreasing b) Any…

A:

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: Given the function f(x) = x2/3, which of the following is a valid formula for the instantaneous rate…

A: fx=x23fx+h=x+h23At x=8f8+h=8+h23f8=823=23×23=4

Q: 4 Given the function f (x) = :3 using the limit shown below. You do not have to simplify your…

A:

Q: Find an equation of the tangent line to the graph of the function  y = log3 x, at the given point…

A: y = log3 x

Q: 12. Consider the function f (x) = sin (nx). On the interval [0,3]. At what value of x would the…

A: Topic = Derivative

Q: 1 If a spherical drop of liquid evaporates at a rate proportional to its area, if initially its…

A: Let the surface area be A So rate of evaporates is dA/dt, According to the question, dVdtαAdVdt=-kA…

Q: Suppose that the population of a certain collection of rare Brazilian ants is given byP(t) = (t +…

A: To find the rate of change of population P'(t), we need to differentiate the function…

Q: Determine the equation of the tangent line to the graph of y = f'(x) at the point where x = 1 if…

A:

Q: If the instantaneous growth rate of COVID19 is modeled by (limHh->0)(200t+100h). At t=5 seconds…

A:

Q: Suppose we have a tank that contain 10 litres of water and 50 g of salt. The salt solution is…

A: given , tank that contain 10liters of water and 50 gram of salt .  so , initial concentration =>…

Q: 2. Given the graph of derivative f'(x), find: a) Any interval (s) where f(x) is decreasing b) Any…

A: the function is decreasing when  as we can see from the graph,  on the interval  and  which means…

Q: The production output of a certain factory is N(t) = √² + 10t + 8 where N(t) is the output in…

A: Given is the production output asN(t)=t2+10t+8 We need to find out the rate at which the production…

Q: If f(x) = 5x-3 Compute the instantaneous rate of change of f(x) at x = 2. OA.7/41 Ов. -3/49 Oc. 1/5…

A:

Q: b) Find the equation of the line tangent to the graph of y=log; (5x +1) at x = 2

A:

Q: A particle is moving on the x-axis and the position of the particle at time t is given by x (t),…

A:

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = In x²;…

A:

Q: It has been estimated that the total production of oil from a certain oil well is given by T(t) =…

A:

Q: Suppose this graph represents the 1st derivative function, f'(x). At what value(s) of x does Ax)…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 2. Suppose that a model rocket blasts off, straight up, at time t = 0, with a vertical displacement…

A: Note: As students mentioned for only 1st part so I solved 1st part.

Q: 4)Find the inflection points of the function . f(x)=ln(x^(2)+1)

A: In this question we will find the point of inflection   we have given function   f(x)=ln(x2+1)…

Q: Find the slope of the tangent line to the exponential function at the point (0, 1). y 2 1 (0, 1) -2…

A:

Q: 2 Refer to the graph above and without making any computa- tions find: The average rate of change…

A:

Q: Consider the following function. h(x) = 5 - 2x Find its average rate of change over the interval [1,…

A:

Q: Find the equation of the tangent line to the graph of f(x) at x = 2, if 25 f(x) = 2.5 + log5 2 (x -…

A: For x=2 f(x)=2·5x+log5252xf(2)=2·52+log5252(2)f(2)=2(25)+log525f(2)=50+2f(2)=52 So the point is…

Q: The volume of a sphere is increasing at a rate proportional to the reciprocal of its radius. At t =…

A: Given that the volume of sphere is increasing at a rate proportional to the reciprocal of its…

Q: Find the derivative of the function. y = log 6 V3x+7 3. O A. In 6 3 In 6 O B. 3x +7 In 6 (3x + 7) 3…

A: Given, y = log63x + 7Applying the log rule; logab = lnblnay = ln3x + 7ln6Differentiating with…

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: Note: You may need to assume the fact that lim 1-0 for all n. MI The number of cell phone…

A: Given problem:- Note: You may need to assume the fact that limM→∞Mne-M=0 for all nThe number of cell…

Q: Find the derivative. y= e at O 4(1/4)x -4(5/4)x In 4 4(3/4)x In 4 4(5/4)x 25 n4 16

A:

Q: Suppose that a factory worker starts to make face masks at t = 0 and his rate of change of…

A:

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: If f(x) = 5x -3 , compute the instontoneus rate of change of Sx) at x-2. OA -3/49 O8.7/41 oc-7/41…

A:

Q: The equation y = log(x + 4) has a vertical asymptote at: %3D X =

A:

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

A: The given function fx=x23 The instantaneous rate of change is given by limh→0fa+h-fah