The limit is equal to -∞ 0-1 01 0 lim x→0 Sln(1 + t²) dt x

Q: Evaluate the definite integrals using substitution 1.) ²3√5x-1dx

A:

Q: Determine the 8-values for the points of intersection of the graphs of the polar curves r = 3 sin…

A: The given polar curves r=3sinθ+1 and r=sinθ. We have to find the point of intersection point of the…

Q: tion true, or explain why it does not exist. (1 + c)" =2

A: NOTE: Refresh your page if you can't see any equations. .

Q: 3. A farmer has a plot of land bordering an extremely straight river bank. The farmer wants to…

A: NOTE: Refresh your page if you can't see any equations. . x=width of the rectangular plot y=length…

Q: 2) Evaluate surface z dv where E is the region enclosed by the Z = x² + y² and the plane Z = 1

A:

Q: If sin x=3/5, x in quadrant I, then find (without finding x) : sin(2x)=___ cos(2x)=___…

A:

Q: Use the Divergence Theorem to evaluate the surface integral F. ds. F = (x³,2, z³), S is the sphere…

A:

Q: Use the graph shown to find the following (a) The domain and range of the function (b) The…

A: We need to interpret the graph.

Q: 4. Find the average value of f(x)=√√x over [-8,1].

A: Given query is to find the average value of function.

Q: Find the Taylor series, centered at c = 3, for the function 1 1 - x² f(x) = (-1)^(4n-3) 8hn! The…

A:

Q: In 10 229ܨ 1

A: Given query is to expand the expression.

Q: Use the graph of y=f(x) to answer the following. Part 1 of 8 (a) Determine /(-4). (-4)=0 Part 2 of 8…

A: given graph of f(x)

Q: = 18. Evaluate SF · dỡ, where ♬ = (eª,xy) and C is the curve parameterized by r(t) = (t², t³), 0≤ t…

A:

Q: Check the convergence or divergence of the following series and find the sum if the series converges

A: We have to find if the given series converges.

Q: The velocity function is v(t) = t² — 5t + 4 for a particle moving along a line. Find the…

A:

Q: Given that f(x) = x³h(x) - h(1) = 5 h' (1) 8 = Calculate f'(-1).

A:

Q: 3. lim x² ln x x-0+

A: Given: limx→0+x2lnx

Q: Rewrite the following in terms of a single logarithm: - log(x+2) - 3 log(x) − 5 log(x² + 1)

A: We are required to write the given expression  log(x+2)-3logx-5log(x2+1) in terms of a single…

Q: Find the equation for the parabola that has its focus at (−35/4,−3) and has directrix x=-29/4.

A:

Q: 1. Bernoulli's Equation. Find a particular solution of the differential equation y^2dx + (2xy -…

A: solution is below.

Q: Suppose that the monthly marginal cost for smokejumper harness straps is C'(x) = 3.5x +95 and the…

A:

Q: Use any method to determine if the series converges or diverges. Give reasons for your answer. 8 Σ…

A:

Q: Suppose that a particle moves along a straight line with acceleration defined by a(t) = t - 5/2 in…

A:

Q: Find the area of a triangle with sides of length 12 and 30 and included angle 78 degrees. wer is

A:

Q: 5. y = (x + c)e*

A:

Q: hape of a box with a square base. It is to have a volume of 686 cubic feet. The concrete for th the…

A:

Q: car travels xm, 7.5m, 11.25m and 16.875m in the first, second, third and fourth minute of its…

A:

Q: A radioactive chemical has a decay rate of approximately 10% per year. Suppose that this chemical is…

A:

Q: The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. y (a) (b) (c)…

A: Let's solve all integral value.

Q: The point x O is a regular singular point of the given differential equation. Find the equation for…

A:

Q: The rate of U.S. per capita sales of bottled water for the period 2007-2014 could be approximated by…

A: given rate is  s(t)=0.25t2-t+29refrence is year 2007 fot 2007 to 2014,   0≤t≤7there for 2009 to 2012…

Q: The daily output at a factory is Q(K, L) = 128K L units, where K is the capital investment measured…

A: Given  Q(K,L) = 128(K)^(3/4) * (L)^(1/2)

Q: Find the area enclosed by the given parametric curve and the x-axis. x = 8 sin(t), y = sin(t)…

A: To find the indicated area

Q: Let u = -3) and v=(5, -2) and w= = (-6, -4). Fin (2, -3)

A: Givenu=2,-3,v=(5,-2),w=(-6,-4) The objective is to find the angle between the vectors 6) angle…

Q: Find the indicated partial derivatives of: дz дх Oz au || || Z= 4x x2+y2

A:

Q: Consider the curve given by x = t³ +2t² - 4t + 7 and y = -8t+t². (a) Find the equation of the…

A:

Q: Find all the values of x such that the given series would converge. Answer: 3 8 n=1 8" (x-3)" n+3

A:

Q: Show that the given curve c(t) is a flow line of the given velocity vector field F(x, y, z). c(t) =…

A: We have to show the following conditions according to the given information

Q: Given: f(x, y) = x³y +exy ² 9. find fxy b. find a³f ayayax

A:

Q: Determine each of the following limits using any technique, 3x-2x x-0 7x-4x b. lim (In(x)) a. lim c.…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Find the values of x, y and z that correspond to the critical point of the functio z = f(x, y) = 4x²…

A: for critical points put  fx=0 and fy=0∂xn∂x=nxn-1∂constant∂x=0

Q: Solve the given LDE using the method of variation of parameters.  (D2+1)y = csc x

A:

Q: The graph of g(u) = - 2u + 2 is given below. + -4 -3 -2 -1 Q Use the limit definition of the…

A:

Q: Show if the following limits produce an indeterminate form. Then, evaluate the following limits.…

A: according to guide line we do only firt part . please re post other part 1)   limx→01+x-1-x2x2if we…

Q: Let f(x) = 4√√x+5x. Verify that f(x) satisfies the conditions of Mean Value Theorem on the interval…

A: Here is the solution:

Q: Find the sum of the following series. If it is divergent, type "Diverges" or "D". n=0 7" 9nn!

A:

Q: 4.) [3x²(x²+2) dx

A:

Q: What is the length of the major diameter of this ellipse?

A: We need to find the length of the major diameter of the given ellipse.      13x2+2x+y2=1

Q: Consider the following parametric curve. Find dy dy dx dy x = sin(4t) + cos(t), y cos(4t) sin(t) 4…

A:

Q: Find the area of region using integral

A: