d (a) / ₁ (t²-1)²dt. -10 -10 (b)/(t²-1)²dt. (c) d dx 32² -10 3x² (t²-1)² dt. d (d) — (t²-1)²dt. dx 4x-1

Q: If the population of an ant colony in 3 days is known to be 2000 and P'(0) 2. What is the…

A: For Linear Growth we have formula, Pt=P0+ktWhere Pt is population at t days.P0 is initial…

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

A: To find the derivative

Q: 9. lim 818 4x + 3 5x − 1

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

A:

Q: 2) Solve the given Variable separable DE 1) x cos² y dx + tany dy =0

A:

Q: Let f be a function defined on [15, 23]. Suppose for every x ≤ (15, 23) d da If f(16) = 44, find the…

A: We  know By definition of derivative  in interval a,b⇒f'x=limx→afx-fax-a

Q: (b) Let rzi+yj + zk, and let r= ||r||. If f is a differentiable function of one variable, show that…

A:

Q: Write an expression for the nth term of the sequence. (Your formula should work for n = 1, 2, ....)…

A:

Q: Determine the vertex, pocus, directrix and axis of symmetry of the parabola with the given equation.…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 37-40 Find y' and y". 37. y = cos(x²)

A:

Q: Determine the solution for the following higher-order nonhomogeneous differential equation. Also,…

A:

Q: If the rate of change of a population is directly proportional to the square of the population and…

A: If the rate of change of a population is directly proportional to the square of the population and…

Q: 1. Obtain the general solution by the indicated technique: separation of variables 1.1…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find f′(x) and simplify.   ​f(x)=1/(x+35)  f'(x)= .....?

A: Differentiate wrt x

Q: The demand function for Wally Winka's Neverending Lollipops is given by p= (12-x)In(x + 7) where p…

A: Given  p=12-x lnx+7 is the demand function When x=6    p6=12-6 ln6+7           =6 ln13   Rate of…

Q: 1. Evaluate the following integrals: 5/2 d. S3 1 1/2 2 2x -x -dx

A: The integral is  ∫1/25/2 12x3-x2dx

Q: Describe (don't sketch) the "level curve" defined by sin(√x² + y²) = 1.

A: Given:      sinx2+y2=1⇒x2+y2=sin-1(1)⇒x2+y2=π2+2πn⇒x2+y2=π24+2π2n+4π2n2

Q: If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) =…

A:

Q: Please show your answers to at least 4 decimal places. Find the directional derivative of the…

A:

Q: Consider the following. 3(1 + 104x) = 8 (a) Find the exact solution of the exponential equation in…

A:

Q: (b) F(t)=(e²¹)i + (2e²¹ +5)j + (2e²¹ -20)k for 0≤1≤ In 2

A: As we know that: The expression for the length of vector-valued curve in the interval a≤t≤b is:…

Q: An object moves with velocity as given in the graph below (in ft/sec). How far did the object travel…

A:

Q: Problem 3. evaluating them. ∞ 1 So₁² (2-3)³/2 5 dx Determine whether each integral is convergent or…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: New question: 37 please as well

A: The given function is; y=xx.

Q: Solve the following differential equation: [e2y − y cos(xy)]dx + [2xe2y − x cos(xy) + 2y]dy = 0

A: e2y − y cosxydx + 2xe2y − x cosxy + 2ydy = 0

Q: Problem 6. that the pattern of the first few terms continues. (a) { 1 1, Find a formula for the…

A: Given Sequence :- (a) 1,13,15,17,19,....... (b) 2,-43,89,-1627,3281,.....

Q: Find the slope of the following lines.

A: see below the answer and calculation

Q: Express each of the following in terms of a reference angle. 29.) a. sin 128⁰ c. sin(-37°) 30.) a.…

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

Q: Consider the following. 62 1 + ex (a) Find the exact solution of the exponential equation in terms…

A:

Q: O TRIGONOMETRIC IDENTITIES AND EQUATIONS Proving an identity using fundamental trigonometric…

A:

Q: Evaluate the following integral in spherical coordinates. 2 /4 4 csco 2 SS S p² sin o dp do de Ο π/6…

A:

Q: -4-x² - y² 4 component. For the function f(x, y) (-3, -3) that has a positive find a unit tangent…

A: Let's find unit tangent vector.

Q: 1. Determine the type of conic section that each general equation will produce. Show your solution.…

A: As per the rules, we are supposed to answer the first question and rest can be reposted.

Q: The function f(x) = 2x³ - 45x² + 300x + 9 has one local minimum and one local maximum. Use a graph…

A: Topic - Local extrema's of a function We are given an equation, f(x)=2x3-45x2+300x+9And it's known…

Q: 2. (a) Draw the graph of f(x) = = 2x x 0 (b) Find lim f(x) and lim f(x) or explain why they do not…

A: follow next step

Q: Crystal is running a picture-framing business. Refer to the given break-even chart for her business…

A: The Solution is given below:

Q: 5e 42 sin(y), find a unit tangent vector to the level curve at the point component. Present your…

A: The function is  f(x, y)=-5e-4xsin(y)

Q: * 36, got 6=-8, 311/2<0² 2π1₁ eSC

A: given cot(∅)=-8tan(∅)=1cot(∅)=-18∅=tan-1-18∅=352.8749837o

Q: Consider the following. 4 + e¹- 4x = 25 (a) Find the exact solution of the exponential equation in…

A: To solve the given exponential equation

Q: Consider the solid obtained by rotating the region bounded by the given curves about the y-axis. x =…

A: The given region is:x=33y ,      x=0    and     y=2

Q: a) b) (2,5,-1). Find the values of a,b in a +ib=(3+i)(2-3i where i=√√-1 Find the position vector…

A:

Q: Why does it make sense to model the monthly temperature with a sine or cosine function? Part 2.…

A: We need to model trigo. function.

Q: Let F(x, y, z) = x³i+y³j+z³k. Compute the following: (i) V.F (ii) V X F

A: i) Given:       Fx,y,z=x3i+y3j+z3k then         ∇·F=∂∂xx3+∂∂yy3+∂∂zz3                 =3x2+3y2+3z2…

Q: Consider the function f(x)= 2x-3 x-1 1. f(x) has a horizontal asymptote at y = 2. f(x) has a…

A:

Q: A function contains the following ordered pairs. ((0, -8), (1, -6), (3, -2), (4, 0), (5, 2)) Which…

A: To find the function: Find a general rule satisfied by all the elements .

Q: 6. 2 S²³ x5 ln x d

A:

Q: How do you evaluate the following integral: Integral of (-sin2(x)) dx I'm tempted to use the basic…

A: As we know the trigonometric identity: cos2x=1-2sin2x And use the common integral:…

Q: dz Given z = xy + sin(xy2), with x(t) = 2t + 1 and y(t) = -t², find dt t=1

A:

Q: [6 6x ln (x + 5) dx

A:

Q: Determine the vertex, focus, directrix and axis of symmetry of the parabola with the given equation:…

A: Given Equation:- 3y2+8x+24y+40=0