Jy csc?y dy is equal to A —у сoty — coty dy - Scon dy у сoty coty dy с) -у соѓу+ coty dy D) None E у coty + coty dy

Q: Ise the function f and the given real number a to find (f-)'(a). (Hint: See Example 5. If an answer…

A: We have to find out the derivative

Q: 25) pind te ered af formed by reusiviny the circie fue su face = 10 cose cbort tue line o= 2 2 a)s…

A: Option C is true

Q: Describe the graph of the equation. r = (6 – 31) i – 81 j O It is a line in 2-space that goes…

A:

Q: The temperature at point (x, y) is given by T(x, y) = 100 – 3x² – y³. Find the direction from point…

A: Given

Q: Problem:

A: answer is in next step

Q: 7. For what values of m does the function y = e™ satisfying the following equation y" – 3y' – 10y =…

A: Here is the solution:

Q: e limit does not exist, enter DNE.)

A:

Q: Use a change of variables or the table to evaluate the following definite integral. 10 e 2X dx 2x…

A:

Q: s(2) dr=3 and s (4)d. f (x)dx: =-2. what is (x)dx? Make sure to justify your answer -2 or the…

A: We can find the answer as below using property of integration.

Q: Given =16,-2,k) and V=14,-4, 0]. Determine the value(s) of k if the angle between ü and v is 60°.

A: We will find the possible values of K as shown below

Q: Find div F and curl F if F(x, y, z) = 9y%z®i – 4x°z1°j – 5xy°k. - -

A:

Q: A particle is moving in a straight line according to the position function s(t) = t³ – 6r² +9t + 5,…

A: Given: s(t)=t3-6t2+9t+5,t≥0 d)After breaking once the velocity of the particle becomes zero.i.e. v=0…

Q: Use the Integral Test to determine whether the infinite series E is convergent. (Use symbolic…

A: We have to find if the series converges.

Q: ||r(t) × r"(t)|| ||M(t)|| Use the formula k(t) to find k(t). r(t) = t²i + t'"j 242 t7 K(t) = (4+ 121…

A: Cross product

Q: x'y" – xy' + y = In(x)

A:

Q: y"ーy=

A: Given problem:- Solve the following differential equation y'' -y=xe-x

Q: d dri(t) • r2(t)] = d [ri(t) × r2(t)] dt ||

A:

Q: Find out whether the series given below converges or diverges. 00 Σ 5n + 8 n = 1 Choose the correct…

A: Comparison Test: Let us consider two series ∑n=1∞un,∑n=1∞vn such that un≤vn ∀n∈N Then ∑n=1∞un…

Q: Water is being poured at the rate of 2z m' /min into an inverted conical tank that is 12-meter deep…

A: We need to find rate of water leaking.

Q: a. Use the product rule to find the derivative of the given function. b. Find the derivative by…

A:

Q: Use a triple integral to find the volume of the region bounded by 5x + 8y, z = 9, and the planes x =…

A:

Q: Use the function f and the given real number a to find (f ¯-)'(a). (Hint: See Example 5. If an…

A: Given:      f(x) = ( x+7) / (x+2)

Q: 8. Describe the type of indeterminate form. Evaluate the limit using L'Hôpital's Rule if necessary.…

A: Since, you have posted multiple questions. As per guidelines, we"ll solve only first question. If…

Q: Suppose a population function P(t)  the following differential equation. P is measured in millions…

A: Given dPdt = P(P-10) The slope field is plotted in Desmos slope field generator

Q: Determine the extreme values of the function f(x) = 2 cos(x) –1 on the interval [0, 27].

A:

Q: Use a double integral to find the volume of the region under the graph of f(x, y) = xy and above the…

A:

Q: (x=1² +3t – 1 + 3t – ; at t=-2. t-2 y = t² +1

A:

Q: Identify u and dv for finding the integral using integration by parts. Do not integrate. In(5x) dx u…

A:

Q: The widths (in meters) of a kidney-shaped swimming pool were measured at 3-meter intervals as…

A:

Q: 1. Find the derivative of the following. f(x)=13x* -7x²+5x²+11x+75 a.

A: Formulas:ddx(a f(x))=a ddxf(x)ddx(xn)=an xn-1ddx(a)=0;  where a is a…

Q: Find out whether the series given below converges or diverges. 00 In (n+ 1) Σ n+1 n= 1 Choose the…

A: Here we will find whether series is convergent or divergent,

Q: Given a = 3 units, = 1 unit and the angle between a and b is 30°, determine o) the exact value of (…

A: Solution:

Q: Find V. (F x G), if F(x, y, z) = 3.xi +j+ 6yk and G(x, y, z) = xi + yj – zk. V· (F x G)

A:

Q: Here is a review question, do you remember how to find tangent lines? Find the equation for the…

A:

Q: Use the figure to give approximate values for the following (if they exist). Enter your answer as a…

A:

Q: Inn 1 1 1 1 + 25 1 1 a) Σ-(-1)" (- b) 1+ 4 1 + 64 n-Inn. 9. 16 36 49

A:

Q: denominator is a binomial.

A:

Q: Clairaut's Theorem Give one example of a function where the Clairaut Theorem fails, and justify your…

A:

Q: Use Theorem 9.11 to determine the convergence or divergence of the p-series. 1 1 1 + 8 1 + +... p =…

A:

Q: The figure to the right shows four regions bounded by the graph of y = x sin x: R1, R2, R3, and R4,…

A: To find the value of the  given integral .

Q: hW (3 Xy'a4Y) dx + (3 X*y'+2x) dy = o I) sin X dy - Sin 2X -y Cos X dx

A: Given

Q: Is) Phd an equetian f te tangerut lme et a point C0.0) on the cur ve X= t-144 Aswers: aj 2y-x>0…

A: Topic = Derivative

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

A: Given: f(t)=-16t2+444t+8

Q: of tue reigon boundrd by the graph of tue algebraic fundin. 2) Find tue asea f(x) = x+12x +36 2 =…

A: Given

Q: 7) find the volume of the solid generated by revolving the region bounded by the graphs of the…

A:

Q: Use only the fact that 3x(2 - x)dx = 4 and the properties of integrals to evaluate the integrals in…

A:

Q: Ql use the gauss elemen tution find? X-3Y+42=D0 2W-2x+3 -b+4X+34-82=0

A: Firstly , write the given system of equation in augmented matrix form and after that apply row…

Q: Answers a) A=7In(so)

A:

Q: Compute the surface area of the cone generated by revolving c(t) = (t², t) for 0 <t < 6. (Use…

A:

Q: EX2 Compute the secand erder partial Jerivative Fx ち,ち~ and a)

A: " Since you have asked multiple  question we will solve first one for you. Please ask specify…