Suppose that interest on money in the bank accumulates at an annual rate of 6% per year compounded continuously. If you deposit $3000 in the account today, how much will it be worth 20 years from now? (Hint: First find the equation that represents the balance B = B(t) in the account at time tyears.) OA. $6775.68 OB. $903.58 C. $10066.36 OD. $10030.45 OE. $9960.35

Q: of f'(1)? Use the chain rule to differentiate f(x) = (x10+ln(x)) 10. What is the value (A) 110 (B)…

A:

Q: Find the area enclosed by the given parametric curve and the y-axis. x = t²_ 2t, y = √t

A: The given curves are: x=t2-2t ; y=t The area is enclosed by x=t2-2t, y=t and y-axis i.e., x=0.

Q: 3. Find the radius of convergence and the interval of convergence of the power series Σ (1-x)n n +1…

A:

Q: Τ ΣΚΑ k=0

A:

Q: Using the Intermediate Value Theorem, show for the function f (x) = x^3 − x^2 + 3 that f (x) = 0 has…

A:

Q: Find the interval of convergence of the series. (5x)n 12" n=1 (Use symbolic notation and fractions…

A:

Q: Differentiate the function. -3 f(x) = f'(x)=[ 3x +2 2x-4

A: To differentiate the following. fx=3x+22x-4-3

Q: Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the…

A:

Q: K Write an equivalent exponential equation. log 256 4 = 1 The equivalent exponential equation is…

A:

Q: (6) In this problem we will determine a formula for the volume of a pyramid with height h and a…

A:

Q: Use the values in the table below to answer each of the following: x h(x) g(x) h'(x) g'(x) 0 2 1 -5…

A:

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

A:

Q: Certain radioactive material decays in such a way that the mass remaining after t years is given by…

A: Given: m(t) = 490e-0.03t, where m(t) is mass remaining after t years. To find: a) Mass at time t = 0…

Q: Create the graph of a continuous function f that has f'(x) given below. Is it possible to create…

A:

Q: Series n=0 5 on top.  n!x^n.   0!=1

A: Solution is given below:

Q: W The dosage for a certain type of chemotherapy drug depends on several parameters of the particular…

A:

Q: Find the derivative of the function. f(x) = (tan³(x) + 2)² f'(x) = [] X

A: to find the derivative

Q: A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the…

A:

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

A: We need to find the limit of the sequence limn→∞cos2n

Q: 3 3 Find ΣΣ2-j3 i=0 j=1 Ο – 99 O-102 Ο 102 Ο 193

A: solve the problem by finding the value of the expression.

Q: For the function below, find (a) the critical numbers; (b) the open intervals where the function is…

A:

Q: Find the Maclaurin Series for the function

A:

Q: The percentage of deaths caused by smoking related heart disease is represented by the function 65(x…

A:

Q: Fill in the missing values such that the final term is pulled out of the summation 1-k

A: We  are asked to find the missing terms of the summation

Q: Indicate the points at which the function shown in the graph above has a global maximum, a global…

A:

Q: A gardener has 840 feet of fencing to fence in a rectangular garden. One side of the garden is…

A: A gardener has 840 feet of fencing in a rectangular garden. One side  of the garden is bordered by a…

Q: The particular solution when x y' = (x² +1)/(2-y) is: -3 and y = 4 of the differential equation

A:

Q: Consider the graph of the function g given by g(x): (Remember that one?) Let A(x) be the area of the…

A:

Q: The region R is the region in the first quadrant bounded by the curves y = x² - 4x + 4, x = 0, and x…

A: First find area under the curve y=x2-4x+4 on interval 0, 4.

Q: Using separation of variables technique, solve the following differential equation with initial…

A:

Q: 4 k '(1) = k '(3) = 3 2 1 0 V 0 1 g(x) 2 3 نا 4 X Let k(x) = f(x). Use the graphs above to find the…

A: The graph is given

Q: Please answer this question asap I will rate you for sure. find integral of…

A: The solution is shown below-

Q: Which of the following is equivalent to 3x²(-2x)e-x² + e-x²16x O -16xe-x²(x² - 1) O 16xe-x²(x² + 1)…

A: Given query is to simplify the expression.

Q: Suppose that f(x, y) = x³y². The directional derivative of f(x, y) in the directional (−1, 1) and at…

A: f(x,y)=x3y2point is (2,-2)in the direction of (-1,1)

Q: Let f(u) = √u and g(x) = u = 4 + 9x². Find (f o g)'(3). (fog)'(3) = (Type an exact answer.)

A:

Q: A = 1 -5 1 -3

A: Given: Find the general solution to the system x'= Ax, where  A=1-51-3

Q: 2) Given f(x) = ax²+bx+c has a y-intercept equal to 5, ƒ"(1)= 16, and (1,11) is a point on the…

A: f(x)=ax2+bx+cy intercept is 5f''(1)=16(1,11) is a point on the curve d dx(xn)=nxn-1

Q: Find the volume of the solid that lies under the paraboloid z = 81-x² - y² and above the unit circle…

A: To find the volume

Q: The graph of the function f(x) is provided above. a) Indicate (i.e. check) all labeled points at…

A: A graph of the function is given, we have to find its global extremum and local extremum.

Q: Question #2 - What is the interest rate of an investment is it takes 5 years to double my…

A:

Q: Solve the system of linear equations. -x+4y+z= 9 x - 2y4z = 9 -2x - 3z = 14 O (-1, 3, 4) O (-1, 3,…

A:

Q: 13-30. Derivatives Evaluate the derivatives of the following functions. 13. f(x) = tan¹ 10x (14.)…

A:

Q: 5. Evaluate the following limits. 1 a. lim X-4+X-4 3-x² x→∞ 2x²+1 b. lim

A:

Q: A mouse named Minnie can run back and forth along a straight path in her cage for 24 hours. On one…

A:

Q: Find an equation of the plane through the point p=(2,1,-4)  and perpendicular to the line x=2+3t,…

A:

Q: derivative f'(x)? Let f(x) = (e +ln(x²))³. Which of the following represents the first (A) 3 (eª +…

A:

Q: A spherical balloon is inflating with helium at a rate of 320* How fast is the balloon's radius…

A: Here we have to find the rate of change.

Q: Evaluate the indefinite integral: [=³√ x³ √√13+x¹dx = NOTE: Don't forget your constant of…

A: Given: ∫x313+x4dx

Q: The density function of X is:  f(x) = c·x2 ·( 1 - x ).  Calculate the mode of X.

A: The density function of X is: f(x) = c·x2 ·( 1 - x ).  Calculate the mode of X.

Q: Determine if the following series is convergent or divergent. 5 * 4n+2 32n-1 * 21-n Σ n=0

A: