Do as indicated. a. Find the equation the tangent line and normal line to the graph of f(x) = x³ at x = 2. Graph the function. b. Find the equation the tangent line and normal line to the graph of f(x)=√x at x = 4. Graph the function.

Q: Evaluate the following limits. 1. lim 1 cosh x x+0+ ln(x² + 1) 2. lim (tanx) (sin x-1) x+7+

A: Let's solve for given limit.

Q: II. Evaluate the following integrals. 1 - coth² (log₂x) dx rcosh (log₂x) 1. S

A:

Q: Set up the triple integral that will give the following: the volume of R using cylindrical…

A: We have to find

Q: Evaluate St dx 0 √9-4x2 a. 0.285 b. 0.123 c. 0.423 d. 0.365 e. NONE OF THE ABOVE

A:

Q: . Calc.   Test for exactness then solve. (2xy - sinx)dx + (x2 - cosy)dy =0

A: Differential equation

Q: ∙1 Ꮭ ᏝᎽ 1-x-y z dz dy dx

A:

Q: Find the volume generated if the area between y = coshx and x- axis from x = 0 to x = 1 is resolved…

A:

Q: Evaluate the limit using the L'Hopital's Rule 1 - cosh x lim x+0+ ln(x² + 1)

A: SOLUTION-

Q: 4 fcos 3x sin³ 3x dx

A:

Q: III. Let f(x) = e2 sinx 1. Use the local linear approximation of f at x = 0 to approximate…

A: Given problem:- Let f(x)=e2sinx.   1. Use the local linear approximation of ƒ at x = 0 to…

Q: Find the absolute extremum points of f(x) = sin2 x + cos x on the interval [0, π].

A:

Q: handwritten. Please skip

A: We assume inf B is the greatest lower bounded of B which means that it is lower bound : inf B ≤x…

Q: -0.03t The function f(t) = 9000 e represents the rate of flow of money in dollars per year. Assume a…

A: Given that,

Q: Scot³ x ( cz) ¹4 dx sec x tan x 5.

A: Follow the procedure given below.

Q: Given two functions F and G, we say that F is an antiderivative of G when O F'(x) = G(x) for all a…

A: Above two questions are answered.

Q: (sinhz)(coth’z+csch*r)dz

A: Integration is done.

Q: answer a and b a. The marginal cost of manufacturing x tarpaulins is given by 0.03x2 + 0.4x + 7. If…

A: Explanation of the answer is as follows

Q: √²2² √(-2² + 1)³ dz

A:

Q: 3. -3 √₁|2 - 2³ | dr da 0

A:

Q: Find the average value of f(x) = -3√x + 5x over the interval [0, 3]. Submit an exact answer using…

A: This question can be solved using the concept of average value of function over an interval.

Q: Electric usage over the course of a day varies. The graph shown is of electricity costs per hour.…

A: Use average concept

Q: IV. A small business determined that the price-demand and cost functions for producing and selling x…

A: This question is related to profit and cost functions, we will solve it using given information.

Q: Find the area bounded by y = 2 - x² and y=x a. 9/2 b. 7/2 C. 5/2 d. 3/2 e. NONE OF THE ABOVE

A:

Q: 3. Solve the differential equation of order one.  y' = csc x - ycot x STEPS: a. Put the equation…

A: Integrating factor of a differential equation of the form, dy/dx +P(x)y=Q(x) is given by, I.F=…

Q: 1. Let f(x) = sin²(x) cos(x) g(x) = sin² (x) cos² (x) h(x) = sin² (x) cos³ (x) ㅠ (a) Plot all three…

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…

Q: Electric usage over the course of a day varies. The graph shown is of electricity costs per hour.…

A:

Q: the Using the shell method, what will be the equation of the volume of solid formed when the region…

A: Using shell method, equation of volume is given.

Q: II. Evaluate the following integrals. -3 3. √²* |2 - 2ª | dx 0 c

A:

Q: 1. Let B = {. What is A. C. B. ( D. cannot identify } and the operation * is defined by the table…

A: To find what element we get after operating the given elements.

Q: 12. We have the following width measurements of 80 meters wide lake Distance: 0 10 20 30 40 50 60 70…

A:

Q: 1. Solve the differential equation of order one. Show your solutions. y' = x - 2y STEPS: a. Put…

A:

Q: IV. Solve the following problems completely. 3 1. Use local linear approximation to estimate √(3.…

A:

Q: Use the First Derivative Test to find any relative extrema of the function. (a) g(x) = 2x³ – 18x

A:

Q: Find the area bounded by y = 2 - x² and y = x a. 9/2 b. 7/2 c. 5/2 d. 3/2 e. NONE OF THE ABOVE A D E

A:

Q: Find the area of the region bounded by x = the horizontal strip. y²+1 and the y-axis using

A: Area between x=11+y2, x=0

Q: Use cylindrical shells to find the volume of the solid generated when the region enclosed by the…

A:

Q: Evaluate f(x³ -x + 1) dx a. 0.250 b. 0.500 c. 0.625 d. 0.750 e. NONE OF THE ABOVE

A:

Q: Suppose that a movie theater has a screen that is 29 feet tall. When you sit down, the bottom of the…

A: Given: θ=Viewing angleθx=tan-137x-tan-18x…

Q: 3. A particle is moving along a horizontal line such that its velocity in m/s is given by v(t) = 2t²…

A:

Q: What is the center of gravity of the solid formed when the plane region bounded by y = x^2 and y=x+2…

A: We need to find center of gravity.

Q: TU (sin³ x)√1 + cos x dx EN

A:

Q: Find by integration the area of the region bounded by the curves y=x2 and y=−x2+4x. Include a quick…

A: Use area under curve

Q: Find the solution of the given initial value problem in explicit form. 1 y' = (1-7x)y², y(0) = 6…

A:

Q: Q3. Evaluate : IL (2) * dy dx

A:

Q: ¹In(1 + x) -dx X

A:

Q: The following differential equation is a Bernoulli equation: 2 dy + = y³ y3 where y = f(t) dt t By…

A: The following differential equation is a Bernoulli equation:dydt+yt=y23 where y=ftBy making the…

Q: Find the area bounded by the curve 2x² + 4x + y - 0 and the line y+x=0 a. 1.000 b. 1.125 c. 1.525 d.…

A: We will first sketch the curve and the line.

Q: The graph below shows the direction field for y' = 6+3 y, and the initial point (to, yo) is shown in…

A:

Q: Evaluate the indefinite integral given below. Provide your answer below: f6e4 tan (2x) sec² (2x) dx…

A:

Q: 2. (² (sin³x)√1+cos x dx

A: