Evaluate the following definite integral. Express your answer in terms of logarithms. In 9 S In 7 In 9 S cosh x 2 9- sinh-x dx cosh x 9 - sinh’x In 7 (Type an exact answer. Use integers or fractions for any numbers in the expression.) dx =

Q: Find the centroid of the region bounded 1 y = 6 sin(x), y ==x, and x = The centroid is at (x, y)…

A: The solution is given below

Q: y = e²+3 dy dx Find dy dx Type sin(x) for sin(x), cos(x) for cos(x), and so on. Use x^2 to square x,…

A:

Q: Expand the function (Express numbers in exact form. Use symbolic notation and fractions where…

A:

Q: etermine the Laplace Transfor f(t) = 3te-5t cos(2t) stands ca

A:

Q: Determine whether the following series converges or diverges. Show your complete solution. 1+ sin²n…

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

Q: II. L' Hôpital's Rule. Evaluate the following limits using L' Hôpital's Rule. 3-x 1. lim 1-3 2-8

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

Q: Evaluate the six trigonometric functions of the angle 6. (a) (b) sin(8) = cos(8) = tan(8) = cot(8) =…

A:

Q: Find the one-sided limit (if it exists). lim 11x² tan ex Step 1 The sign of the value of x² is…

A: To find the one‐sided limit if it exists.limx→12+ 11x2 tan πx

Q: A tank originally contains 100 gal of fresh water. Then water containing lb of salt per gallon is…

A: Basic differential equation is used

Q: The photo above shows a graph of O Relation D Function C.

A:

Q: (1) Which is the correct formula for finding the derivative of the product of two functions? (fg)' =…

A:

Q: Find an equation of the line that passes through the point and has the indicated slope. Point Slope…

A: Given that , Point =-3,5 Slope m=-34 Find the equation of the line.

Q: Ⓒ giver fixt 4 2 M + 2 as Find the integral y fam be fou half, of a circle. an [0,7].

A:

Q: Use the rational zeros theorem to list all possible rational zeros of the following. g(x) = - 10x³ -…

A: The given polynomial gx=-10x3-8x2+8x-4

Q: Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the…

A:

Q: The length and width of a rectangle are measured as 38 cm and 34 cm, respectively, with an error in…

A:

Q: 2 Y ² = X₁ X=2 AOR LATUS RECTOM

A: Given y2=x

Q: please explain how do we answer the question attached. Do we need to use a calculator?

A:

Q: What is the area of the region between the curves 3 y = x³ and y = x², from x = -3 to x = -1? Select…

A:

Q: The Normal line at the point (0, –1, 1) to the 3 surface exy - xy² + z³ = -2 is 7=y+1=² Select one:…

A:

Q: Differentiate d/dx  ∫ [cos(x), 0] t dt (using the Fundamental Theorem)

A: Differentiate d/dx  ∫ [cos(x), 0] t dt (using the Fundamental Theorem)

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. =x²+²x≤x≤1 3x 2…

A:

Q: Consider the following. y 4 3 Find its foci. 2 1 -1 -2 Find an equation of the ellipse. smaller…

A: we need to find the equation for ellipse

Q: If zis implicitly defined as a function of x and y by xy-yz+xz=0, find dz/dx. (y+z)/(y-x)…

A:

Q: Find all values of c such that fis continuous on (--,-). f(x) = {7-2², c=2.193 c= 3.193 7-2²³, xse…

A: The given function,    fx=7-x2,x≤cx,x>c

Q: If a company spends r million dollars on research, it sales will be s million dollars, where r and s…

A:

Q: 1. Rewrite log(100) = x as an equivalent exponential equation. 2. Rewrite 4* = 64 as an equivalent…

A: 1  log100 = x equivalent exponential function  for exponential function we take both side…

Q: Question 2 a. I b. | function f(x, y) = y² − x² + — a 1 Find the critical points of the function…

A:

Q: Evaluate the integral using the following values. 6 6 6 [°x³ dx = 260, ["x dx = 10, [° dx = 2 + 6 (³…

A:

Q: Find a particular solution to the differential equation Ур = -6y" - 5y'-y = -(t² + 2t + 2e²t).

A: To find a particular solution to the differential equation.-6y''-5y'-y=-t2+2t+2e2t

Q: Let f(x) be defined by f(x) = 3x² + 5x + 2. Find the slope of the tangent line to the curve y = f(x)…

A:

Q: find the derivative of V(t)=260e^(0.6298t

A:

Q: Wallis Formula Evaluate the following integrals. sin (3x) cos5 (3x) dx 1. 2. 16 4 [*³* sin³(2x) dx

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

Q: e2+8i = a + ib, where: a = b i = i

A:

Q: Q5 100 5+2³+ [In(In r)] lim a) 1+ 7 +6² + [In(In x)]200 cos x ln(x-7) *-+*+ In (e-e) b) lim

A:

Q: Find Magnitude and Direction (Angle) Giving the Vector Given the vector u = -47 +17, find the…

A:

Q: ΣΕΠλη της 9 - 515 +1 _h=1

A:

Q: x² = 2y²(y-1) y² = 2x²(x+1) x² = 2y²(y+1) y² = 2x²(x-1) dx (3x²-2-²) 4

A:

Q: Find the derivative of f (y) = 9 tan (y) V 2 12 y³√√

A: To find the derivative of the below expression. fy=9tany−y2−12y3y

Q: A vector with magnitude 9 points in a direction 160 degrees counterclockwise from the positive x…

A:

Q: A spring is stretched 6 in by a mass that weighs 8 lb. The mass is attached to a dashpot mechanism…

A: Given :The spring is stretched 6 in by a mass that weighs 8 lband damping constant…

Q: cos x ln(x - *) *-+ In (e-e*) 6. lim

A: Topic:- limits calculus

Q: Find the general solution of the following differential equation. y"+11y12y = 0 NOTE: Use c, and ce…

A:

Q: From this graph, Find the volume around the X-axis (Use π = 3.14). y = x (0, 0) (1, 1) y=x² R

A:

Q: Perform Basic Vector Operations Given d = (-5, - 10) and b = ( − 3, 3), find ||ď – 6|| and ||ď || –…

A: This is a problem related to vector operation. Please follow the procedure given below.

Q: In Problems 13-16, graph the constant-cost lines through (9, 9) and (12, 12). Use a straightedge to…

A:

Q: The integrating factor of the given DE are already given below. What is the value of “n” ?…

A: We need to find n.

Q: Differentiate y = sec a tan . y' -

A:

Q: Find the smallest number n of terms needed to obtain an approximation of the series 10-6. Hint:…

A: To find the smallest number of terms needed to obtain an approximation of the series

Q: Three different forces act on an object. They are: F₁ (8,5) (1,7) F₂ F3 (0, 3) = - = Find the net…

A: The three forces are given as: F1→=8,-5 F2→=1,7 F3→=0,3