Find the first partial derivatives of the following: ∙i. f(x, y) = tan(3x − y) + - ii. g(x, y) = xy iii. f(x, y, z) = log₂ (y)-xz² r

Q: 2. Find the general solution of the following differential equation: (x² + 1)y' + 6xy=x a. y=1/3 +…

A: Given differential equation ( x2 + 1 )y' + 6xy = x

Q: Find the most general antiderivative. -4x² - 4x+ + C 0 号净化 + C 3 36 1 5.5 dx 0号北 6x 3x3 蛋言人 •…

A:

Q: 10. An ellipse has foci (-4-√15,3) and (-4+ √15,3), and its major axis is 10 units long. Find its…

A: given that focci of ellipse is  (-4-15 , 3) and (-4+ 15, 3) and its major axis is = 10  then we have…

Q: Question 19 If f'(x) = cot² x + 1 and f(1) = 1, then ANSWER: Blank 1 Blank 1 Add your answer 1 f(0)…

A:

Q: 3) Solve 24x-8 = 16 without using a calculator. 3 4) Separate log₂ (√x²√) into a sum of logarithms.

A:

Q: 16 Co C D If u=lnx, then A B [² 1 2 5² 1 So e 2 1- (lnx) (1-u²) du (1-u) du © ²³ (1 - 1²) u ) du e2…

A: The given integral is [1-(ln x)2]/x, limit from e to e2.

Q: b) Let f(x) = 2e-x². Find the intervals at which the function f is concave up or down and find the…

A: Let fx=2e-x2. To find the intervals at which the function f is cancave up or down and to find the…

Q: - 5 = 24 + Z = -1 2x + 34 = 2 -y-2Z = (Mabrices), find of Z Ron Rescaling

A: The given system is: -x-2y+z=-12x+3y=2y-2z=0

Q: Q3 a. In an oil rig a thermodynamic system, K = A TAS-AH RT where R, K and A are constants Find " dk…

A:

Q: √² xdx + ydy + zdz where C is the line segment from (3, 2, 4) to (4, 3, 7). Evaluate

A:

Q: aluate the definite integral by interpreting it in terms of areas. 6 (2x - 8)dx

A: Given query is urgent find the value of integral.

Q: Determine: d O O a) cosx b) sinx d[So cost dt] c) -sinx ( d) cosx-1

A:

Q: 4 Label the vertices, foci, and asymptotes on the graphs given for the hyperbola. x² y² 42 b. -=1 3²…

A: Foci of hyperbola are the two points on the axis of hyperbola and are equidistant from the center of…

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If the…

A: Given query is urgent find sequence converges or diverges.

Q: 1. ſ(x² + x)(xª + x−¹ + 2)dx

A: We can evaluate the given integral in the below steps.

Q: Evaluate the Dot Product u * (v + w). If : u = (-5, 7) v = (1, 6) w = (-11, 2)

A:

Q: lim h-+0 (sin h)/h- cos h h²

A: Evaluate the limit using Maclaurin series limh→0sinh/h-coshh2=?

Q: Perform a first derivative test on the function f(x) = 2x³ + 6x² − 48x+6; [− 4,6]. a. Locate the…

A: Maxima minima

Q: I sir sin3x (csc 3x - cos ³3x) dx

A:

Q: Express the sum without using sigma notation. Simplify your answer where possible. 210920(+1) log10…

A:

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

A:

Q: Use chain rule to find x² √y a. Z = əz at r with x = 3rt and y = = ppir

A:

Q: 1. Find a, b, c, and d such that the curve y = ax³ + bx² + cx + d has its tangent line at (1, 1) and…

A:

Q: Find a Cartesian equation for the curve. ² cos(20) = 81 Identify the curve. hyperbola line ellipse…

A:

Q: Solve the linear program graphically. Use the included graph. Maximize p = x - 2y Subject to: x + 2y…

A: To find solution of given linear programming problem.

Q: A trapezoid has one of its legs perpendicular to both parallel bases. If the altitude of the…

A: According to question,Given,Height of Trapezoid, H = 3 units.

Q: Let y = sin(4x). If Az = 0.1 at z = 0, use linear approximation to estimate Ay Ay = = Find the…

A: Given that , y=sin4x Estimate ∆y using linear approximation and find the percentage error.

Q: Consider a triangle of adjacent sides a and b with as the included angle between these two sides. a…

A:

Q: Solve the following DE: y'=y-xy³e-2x Oe² = y(x²+C) O e²x=y²(x²+ C) Oe-2x = y²(x+C) Oe-²x = y²(x²+ C)

A:

Q: 165. Use Green's theorem to evaluate S (y² + x³) dx + x^dy, where C+ is the perimeter of square [0,…

A:

Q: Find all solutions of the equation 3 sin² x - 7 sin x + 2 = 0 in the interval [0, 2). The answer is…

A:

Q: Show that the following series are convergent and find their sums: a) 1ײ×3 +2×3×4 +...+ n(n+1)(n+2)…

A:

Q: 1 n Prove that 1+ 2+ -3+ + 2-1 (Hint: Differentiate both sides of the equation equation.) +4. 1 1-z…

A: The solution is given below

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If the…

A:

Q: Find the Wronskian of the following vector functions: u(t)= 5t-4 -t · -| V v (t) = -t+4 5t

A: Let  ϕ1(t)  and ϕ2(t)  are two vector valued function  Wronskian of these  vector functions is…

Q: 2 (1+x)²d=1+y²

A: According to rules... I need to solve first question when multiple questions are posted So please…

Q: Find the nth Maclaurin polynomial for the function. f(x)=ex, n=5 Ps(x) = x

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

Q: If sin(θ)=4/7, and θ is in quadrant II , then find cos(θ)=  tan(θ)= sec(θ)= csc(θ)= cot(θ)=…

A:

Q: Evaluate the given integral by making an appropriate change of variables. <-8y 1₂ dA, where R is the…

A:

Q: APPLIED CALCULUS (UPVOTE WILL BE GIVEN. PLEASE WRITE THE SOLUTIONS LEGIBLY. NO LONG EXPLANATION…

A: We need to find out the vertical and horizontal asymptotes.

Q: 11. Which of the following equation is a variable separable DE? a. (x+x²y) dy = (2x + xy²) dx b.…

A: Given,           Which of the following is a variable seperable DE           a x+x2ydy=2x+xy2dx…

Q: Please help with part b

A: We will find the required sum.

Q: 184. Use Green's theorem to evaluate line integral z²ydä – xy²dy where C is a circle x² + y² = 4…

A: The given line integral is: ∫C x2y dx-xy2dy     where C is: x2+y2=4

Q: dy Find and dx dy dx || d²y dx² x = et, y = te-t d²y dx² For which values of t is the curve concave…

A: dexdx=exd dx(ab)=bdadx-adbdxb2dydx=dydtdxdt

Q: The rate of growth of a fish population was modeled by the equation 90,000e-0.6t (1 + 5e-0.6t) ²,…

A: Given the rate of growth of a fish population was modeled by the equation G( t ) = 90000e-0.6t( 1 +…

Q: The final should be 4 no? Not 23/6?

A: Given Vector:- F→x,y,z=lnx+y+xzπ,1+yzsinhy,zey-cosz

Q: xdy dx - 4y = x6ex

A:

Q: -24 t Y 24 ln(8t) — 31 = Given x = (i) (ii) dx dt dy dt = = + 147 and (iii) dy dx the simplified…

A:

Q: m of linear equations x +y = 3z = 2 2x + 3y + 2 = 0 3x + 4y = 2 =1 using 23 the

A:

Q: The zero-order Bessel equation is X²y''+xy'+x²y = 0 Show that X = 0 is a regular singular point,…

A: