Compute the Laplace transform of 10 + 5t + t2 – 4t3

Q: The population of a city is 75,000. If the population is declining continuously by 3.7% per year, in…

A:

Q: The displacement (in meters) of a particle moving in a straight line is given by s = 2t3 where t is…

A:

Q: 2. Find the extreme values of on [-2,2]. f(x) = Sve™, | 2x³ – 9x² - - x 0

A: Solve

Q: The rate of change of the temperature, r(t), in an oven (in degrees Celsius per minute) t minutes…

A: To find out the temperature change using simpson rule.

Q: Find the equation of the family of curves whose slope at any point (x,y) is given and which passes…

A: To find the equation of family of curves whose slope is given .

Q: the velumg of a Gale ungtrude) finm a agn by Caffing tolume of 54d a Tozt Ximia laca of Card toud…

A: We need to maximize volume.

Q: 1. Several statements about the definite integral of a continuous function f(x) over [a, b] are…

A:

Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

A:

Q: 2. Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 – x²…

A:

Q: 3. Find an equation of the tangent plane at P = (0, 3, –1) to the surface with equation ze" + elz+1)…

A:

Q: 5. a. Evaluate lim(3x³ +7x−16). b. What is the meaning of this value?

A: Given;  limx-2(3x3+7x-16).

Q: Consider the curve parametrized by x www = 1 + ln(t) and y = t¹ + 2t. dy a) First eliminate the…

A: topic - derivatives

Q: The decay rate for a radioactive isotope

A:

Q: Evaluate the integral. (Use symbolic notation and fractions where needed. Use C for the arbitrary…

A:

Q: Find the indefınite integral and check the result by differentiation. Find the antiderivative whose…

A:

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 3 1 lim tto0 2t2 +3' 2t (?,?)

A:

Q: Evaluate the integral of the following using Miscellaneous Substitution 3. x /x*+ 1dx

A:

Q: If √√x + √y = 10 and y(9) = 49, find y' (9) by implicit differentiation.

A:

Q: Q8/ A tank contains 100 gal of fresh water. A solution containing 1 lb/gal of soluble lawn…

A:

Q: 1.) lim 5-x 2.) lim 5-x 3.) lim 5-x

A: Given query is to find indicated limit.

Q: Evaluate (sin² (sin² x cos x)(1+ sin z cos x) dx.

A: Use substitution method

Q: 3. A snowball is rolling down a hill, getting bigger as it goes. Assume the snowball remains a…

A:

Q: Is there a number a such that the following limit exists? (If an answer does not exist, enter DNE.)…

A: Given;  limx--2 (4x2+ax+a+12)/(x2+x-2).

Q: An isotope of the element erbium has a half-life of approximately 9 hours. Initially there are 7…

A:

Q: 10. At what point on the parabola y = 3 x 2 + 2xisthetangentlineparallel totheline y = 10x -2? Use…

A: Given query is to find the point where tangent line to the parabola is parallel to the given line.

Q: The car you are interested in has 16 color options, 3 engine choices, and 6 entertainment system…

A: Given ,  The car you are interested in has 16 color options , 3 engine choices , and 6 entertainment…

Q: 15. Indefinite Integrals (Part 1) -/3 -2 a) + cscxcot x dx b) cosx--sinxr+4csc², sin x+4csc² x dx 3…

A: Solution is done in step 2

Q: 2x-5y ≥10 y-axis 4 3 2 1 -54-3-2-1 1 2 3 4 5 6 6 5 N -3 -4 -5 -6 x-axis

A:

Q: Consider the following equation. Step 2 of 2: Find the slope of the tangent line at (-1, 2). 2x² +…

A:

Q: Find the area of the region lying to the right of x = y² + 13y + 14 and to the left of x = 5y + 2.…

A: Area bounded by the curves :  If f(y) and g(y) are two continuous function on a,b and f(y) ≥g(y) on…

Q: 1.57 1 (1.5,2) (-0.7,02) (0.7,0.2) -1.5 -0.5 1 1.5 --0.5+ -1.5 Where does f have absolute minimums?…

A: Recall:  In graph, y-coordinate at the lowest and highest points are called the absolute minimum and…

Q: What is the summation from n = 1 to infinity, of  (3^(n+1)) / 5^n + 1 ?

A: Given that,       ∑n=1∞3n+15n+1

Q: Evaluate each of the following definite integrals 4 |x- 3| dx (x2 - х) dx х2 +x+1

A:

Q: Consider the plane curve given by the parametric equations x = t² + 3t - 26 y = t² + 3t - 28 - What…

A:

Q: 2. Calculate the following transcendental integrals: a) S² exee* dx X b) S (x²+1)In (x²+1) dx cos…

A:

Q: After the release of radioactive material into the atmosphere from a nuclear power plant in a…

A:

Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. (a) Find a vector parametric equation for the parabola y =…

A:

Q: full

A: We will find the polar equation.

Q: A bottle of milk initially has a temperature of 79°F. It is left to cool in a refrigerator that has…

A:

Q: 1 Andrea deposited $5,000 into a 30-year retirement account which compounds continuously. If she…

A:

Q: Find the extreme values of on [-2,2]. f(x) = Sre™, x 0

A:

Q: Find the inverse of f(x) = 3 √5x² +2 What is its domain?

A:

Q: Write the integral in terms of u and du. Then evaluate. u = 812 + 1 (Use symbolic notation and…

A:

Q: Find a polynomial with integer coefficients that satisfies the given conditions. R has degree 4 and…

A:

Q: Consider the curve defined parametrically by x(t) = cos(t), y(t) = sin(t), te [0, π] (a) For what…

A:

Q: lim f(x) and lim f(x) both --3+ r-3-

A: We have to consider the given statement is true or false according to the given information

Q: Evaluate the definite integral. i+ej+tk)dt O es - 1 -- (-~" - 1) + 5 O es i- e- 5 O es i + (e- - 1)…

A:

Q: Find T(t) and N(t) at the given point. r(t) = 4 cos(t)i + 4 sin(t)j; t = 3 r() - () V3 1 T .3 2 2…

A:

Q: In Exercises 33-42, determine if the given vector field has a potential. If so, find one. 34.…

A: Solved below

Q: 6 Find the derivative of: 9/x

A: