Use l'Hôpital's Rule to evaluate the following limits. In(x) I 2x2 - 3x + 1 xx x² + 4x - 1 1. lim x →∞ 2. lim Number Number

Q: List all of the possible rational zeros for the function f(x) = 4x² − 3x³ + x² − 6 H Normal Enter…

A:

Q: Find the equation of the curve for the given slope and point through which it passes. Use a graphing…

A: equation

Q: Express these decimals in short form using the bar to designate the repeating part. Find the…

A: We can solve this as follows:

Q: 9. At time t= 0 a particle is at the origin. It then begins moving along the positive x- axis so…

A: For part (a):

Q: Find a plane containing the point (1,4,3) and the line of of the planes 7x + 5y - 8z = 27 and 5x +…

A:

Q: A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of…

A:

Q: d dx Prove that (csc(x)) = -csc(x) cot(x). d dx (csc(x)) = || = = d dx sin²(x) 1 sin(x) 1 -csc(x)…

A:

Q: Complete the parametric equations of the line through the points (8,4,3) and (-6,-8,-7) r(t) = 8-14t…

A:

Q: Find the gradient of the function at the given point. Function Point f(x, y) (4, 5) Vf(4, 5) = x +…

A: Given function:- fx,y=x+5yy+1

Q: Evaluate the indefinite integral. Answer = +C tan¹(42) de

A:

Q: Use the graph M of the derivative of f to locate the critical points zo at which has neither a local…

A: see below the answer and explanation

Q: 2. a. Write a degree 3 polynomial in factored form with integer coefficients with zeros 6/and. b.…

A: Given :- Zeros of degree 3 polynomial are 6i and 45

Q: Problem #3: Find the work done by the force F = 9xy i+ 12y2j acting along the piecewise-smooth curve…

A:

Q: Use l'Hôpital's Rule to find the limit. In (x²+7x) In x lim X→0* lim X→0* In (x² +7x) In x = (Type…

A: K=limx→0+lnx2+7xlnxd dx(xn)=nxn-1d dx(lnx)=1x

Q: Which of the following numbers is imaginary? A 3+(-√18) B √(-3)(-4) C -√2+√√-4+7 D 5-√6-8

A:

Q: Find the distance from the point (-5,1,2) to the line a(t) = (-5,0, 3)t + (-7, 1, 5) -

A: According to question,Given Point : -5,1,2,Given Line : a⇀t = -5,0,-3t+-7,1,-5

Q: Find the absolute extreme values for a(z) = 6 - 476 on [1,2].

A:

Q: Find the angle of inclination of the tangent plane to the surface at the given point. x² + y2 0 = =…

A: Given query is to find indicated angle.

Q: Find [[ cos (x² + y²) dA where D = {(x, y) | 9 ≤ x² + y² ≤ 25}

A: We need to evaluate :

Q: count in a bacteria culture was 900 after 15 minutes and 1800 after 30 minutes. Assuming the count…

A:

Q: The diagram above shows the graphs of y = e-* (red) and y = x (blue). (a) State the equation in x…

A: Point of intersection refers to the point where the graphs intersect. Graph is a diagrammatic…

Q: Use the limit definition of partial derivatives to find fx(x, y) and f(x, y) f(x, y) = x² - 2xy + y²…

A:

Q: 2. All multiple choice must include work or worded explanations. 1 g(x) dx = 5, then [₁8(x) dx = -…

A:

Q: Find the directional derivative of the function at P in the direction of v. g(x, y) = √√√√x² + y²,…

A: Given: gx,y=x2+y2, p7,24, v=3i-4j   As we know the expression for the directional derivative of the…

Q: 23. What statement is not true? f(x) = #+3 if z>0 if a ≤ 0 a. limf(x) = 3 x →0* b. limf(x) = 0 _0个x

A: f(x)=x+3   if x>0-x     if x≤0

Q: Find the differences in the given base. 51 six (a) (b) (c) (d) 22 six six 501 six 222 six six 753,…

A:

Q: Evaluate lim x-0 e-1 X

A: We have to slove above limit problem

Q: √ x2 (4x² + x² − 1) ³. Find the derivative of f (x) = =

A:

Q: 2. Locate the absolute extrema of the function g(x) = x² - 8x + 12 on the closed interval [0, 5].…

A: g(x)=x2-8x+12d dx(xn)=nxn-1d dx(constant)=0

Q: 1 I 1 1 1 1 I I 1 I 1 1 1 1 I 1 1 1 I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 1 1 1 1 I I I…

A:

Q: In the Google sheet, o Create a vector 'r' of values of the radius of a cone with values starting at…

A: Sl no Radius (r) Height (h) Volume (V) 1 8.9 6.4 530.6013867 2 8.6 6.4 495.4333867 3 8.3 6.4…

Q: Find the eigenvalues and a corresponding eigenvector to the matrix: -2 3 A=(7²8). 10

A: Form the characteristic elation and solve to get eigenvalues and the corresponding eigenvector.

Q: For each function, use our techniques to sketch the graph. Include asymptotes, at least one…

A: (a) Given that,              y=xx-1 x-intercept:            y=0 ⇒xx-1 = 0           ⇒x=0…

Q: 3 Integrate f(x, y) = y(x² + y²)³ over the domain x² + y² ≤ 25, with y ≥ 0. Added 55 Pak Young FGS…

A:

Q: Please help me with every question :)

A: Here we have to choose the correct option.

Q: Consider the following graph of the second derivative, f" (x), for some function f (x): f"(x) 9- 6-…

A:

Q: lim X-70 3√√x+1-1 X

A:

Q: On which interval f(x) = -2³ + 3x² - 4 is concave upward? O a. (-1,1) O b. 1 Od. >1

A:

Q: f(-1)=0 and g(-1)=-1  a. (f+g)(-1), b. (f-g)(-1), c. (fg)(-1), d. (f/g)(-1)

A: Given query is to find indicated function operations.

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of PQ.…

A:

Q: they​ occur, for the function f(x)=x2−18lnxon the domain [1,11].   Select the correct choice below​…

A:

Q: Consider the four graphs shown below. For each graph, select Yes if satisfies the following…

A:

Q: 14. Evaluate the limit for the graph: lim f(x). x → 1 4 a. +∞o b. 1 T y4 4 2 20 +2 T 2 4 c. 3 d.…

A: see below the answer and explanation

Q: 3.) Find the volume of the solid whose base is the region bounded between the curve y=x²-x-3 and y=x…

A:

Q: Can i still answer this without using the l'hospital rule? If yes, can you show me the alternative…

A:

Q: Given Cost and Revenue functions C(q)=q3−11q2+55q+5000 and R(q)=−3q2+2400q​, what is the marginal…

A:

Q: find the revolution of the solid of revolution generated by revolving the region bounded by y=ln(x)…

A:

Q: Find the absolute extrema if they​ exist, as well as all values of x where they​ occur, for the…

A:

Q: Find the length of the arc of the curve Y = 3/2 (2 x − 1) ³ from = - x = 0 to x = 9 - x =

A:

Q: Solve the given differential equation. dy + In xy dx = (10x + In y)dx y=0

A: