Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. sin(x – 1) lim x→1 x³ + 4x – 5

Q: completely

A: We will solve the integration.

Q: Use series to evaluate the limit. X-In(1 +x) lim

A: Find your answer below

Q: S (1/(X(Im)*) dx X(Inx)

A: LetI=∫1xlnx2dxLet u=ln(x)differentiate 1xdx=duI=∫1xlnx2dx.I=∫1u2du.I=∫u-2duUse power…

Q: Consider the system of differential equation x' = 5x – 3y - y' = 9x + 9y Write the system in matrix…

A: To find the matrix A.

Q: Evaluate the definite integral. 12t dt O el2 – 1 (e-) - 1) + 2 – 1 i - (e" - 1) j +k 12 O el2 12 O…

A:

Q: The area of the region is. (Type an exact answer, using x as needed.)

A:

Q: Calculate the following derivative if f(x) = 5e* - x³. %3D (Use symbolic notation and fractions…

A:

Q: Problem 11. Solve the following system and express your solutions (if any) as individual ordered…

A: 3x2-2y2=-5     2x2+4y2=18

Q: Calculate ri(t)· r2(t)] and ri(t) x r2(t)] first by differentiating dt dt the product directly and…

A:

Q: Find div F and curl F if F(x, y, z) = xz°i + 2y°r*j+ 6z*yk. div F=2° + 16 y' x+ 12 zy curl F=

A:

Q: If the tan x 1.5 then what are equivalent expressions to cot x ? Select all that apply. 1 1.5 3 1…

A:

Q: Solve the system of differential equations.

A:

Q: Find the roots Lzerel of eah tunction and State tHhe multipicty of any veputed root - 니 2x

A:

Q: ) (2xy+y2) dx - 2x2 dy = o 2) xy dx-(x + zy)? dy = o メ+ 2y)? dy

A:

Q: FInd Fas a function of x and evaluate it at x = 0, x = 7T/3, and x = /2. FX) = F(x Cos 8 de Fx) FO)

A:

Q: Q3 : prove that : cosh?x + sinh²x =coch2x

A: L.H.S.:=cos h2x +sin h2x=(cos hx)2 +(sin hx)2  =ex+e-x22+ex-e-x22=14(ex+e-x)2+(ex-e-x)2

Q: S V25 – 4x²

A: For the solution follow the next step.

Q: dx (2x2+1)2

A:

Q: Find the are lengtu of tue graph 10) of the fenetian y= x+5 over the imiterval [12, 14]. Anwens a) §…

A:

Q: t3 – 7t2 + 16t –- 12 t4 – 4t3 + 4t² 5. lim t2 w? – 4w + 1 6. lim w-00 3w2 + 7w – 4

A: limt→2t3-7t2+16t-12t4-4t3+4t2

Q: Use a truth table to determine whether the two statements are equivalent. (p v q) a r and p v (q A…

A: Here we have to find the truth table.

Q: 6. v(y) = In (y² – 8y – 1)

A:

Q: cion 3 of 10 plicies t Attempt in Progress curl (9z i + 10x j + 6y k). (9z i+ 10x j+ 6y k) = ( i )i…

A: Topic :- vector algebra

Q: Change the Cartesian integral to polar coordinate | +y*)dx dy

A:

Q: dx sinxtanx

A:

Q: Question 8 of 10 View Policies Current Attempt in Progress Find r'(t). r(t) = (tan(9t))i+t cos(t)j…

A:

Q: 9. (D² - 1)y = 2/(e – e-*).

A:

Q: dw given w = a2 + 2y2 + 22 and a = cos (st), y = -2s Int and Use chain rule to find 2 = 3s' Vi.

A:

Q: Question 2 x2 Consider the function f(x) = x² –1 " (a) Find the intercepts of the graph of f (if…

A:

Q: Find div F and curl F if F(x, y, z) = xz³i+ 4y°x²j+ 6z²yk. div F= curl F =

A:

Q: Find div F and curl F if F(r, y, z) = xz'i+ 4y*x*j+ 62²yk. div F= curl F=

A:

Q: Describe the graph of the equation. r = 2 cos t i- 10 sin t j + k O An ellipse in the plane x = 1,…

A: Parametric plot÷

Q: Find the value of the series: 1+2" 3n-1

A: We have to find sum of series.

Q: 1 dx X +x13

A:

Q: short

A: Please refer to the image below

Q: Determine the convergence or divergence of the series. (If you need to use

A: answer is in next step

Q: dx x?(4x++9)Z

A: Integration are simplyfied..

Q: 1. S 2xe2*dx

A: Given that,   Using integration by part

Q: dy for x'e*y Find dx sin' ( 3x) + In (y) by using implicit differentiation.

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Evaluate the following limit using Taylor series. 7 7 tan -(x) – 7x + lim 4x° 7 7 tan "(х) - 7x +-…

A:

Q: Sy³/y² + 9dy

A: ∫ y3y2+9dyLet u=y2+9=∫u2-9u2du=∫ u4-9u2du=∫ u4du-∫ 9u2du=u55-3u3Substitute back…

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A:

Q: a) Determine whether the series 11n? + 8n + 32 is n³ + 3n2 – 7n + 1 n=1 RY convergent or divergent.

A: Since you have posted multiple questions which are not interlinked i can do first question as per…

Q: Find the minimum speed of a particle with trajectory c(t) = (t3 – 4t, t2 + 1) for t > 0. Hint: it is…

A:

Q: estion 6 of 10 w Policies rent Attempt in Progress Find V (V × F) if F(x, y, z) = 8 sin xi + 3…

A: We know divergence of curl of any vector function is zero.

Q: Evaluate the definite Integral. Use a graphing utility to vertfy your result. dx Step 1 To evaluate…

A:

Q: Evaluate the area of the region bounded by y2 = x and y2 = 6−x.

A: To find : Area between y2=x and y2=6-x First let's find the intersection points x=6-x⇒x=3 Therefore,…

Q: Evaluate the limit using L'Hospital's rule 4* – 97 lim

A:

Q: ||r(t) × r"(t)|| ||r(t)||³ Use the formula k(t) = to find k(t). r(t) = 4 cos(7t)i + 4 sin(7t)j + 3tk…

A:

Q: Consider the following. z = x2 + y2, x = 4s + 8t, y = s +t az az and as Find by using the chain…

A: Here, the given functions are: z=x2+y2, x=4s+8t, y=s+t So, z is a function of x and y and x and y…