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Calculus Questions
Sketch the regions enclosed by the given curves. Decide whether to integrate with respect to x...
find the maximum, minimum and point of inflexion of f(x)= ((x^3)/3) - x^2
For the function y(x) = 3 2 x 2 − 5x + 1: a) Determine the...
two vectors equal⟨1,−3,−2⟩andv=⟨−2,−1,−1⟩determineaplanein space. Without using linear algebra and or row reduction, determine whether the following...
A spherical balloon is being filled with helium at the constant rate of 16πdm3/min. Calculate the...
Set up each problem to be solve using both disk/washer and shell method. Identify which is...
What are the equations of the tangent and normal lines to the following curve: y2+y+x=arctan2(sin3(x)) at...
In a study prepared in 2000, the percentage of households using online banking was projected to...
The demand function for a certain brand of CD is given by p = −0.01x^2 −...
9a. Find a set of parametric equations for a circle with a radius of 3 centered...
The length ℓ, width w, and height h of a box change with time. At a...
Using langragrean, Find the values of x, y and z that minimise (x^4 + y^4 +...
Consider the graph of the function z=2x-3y+c in a plane. In case of c=4, find three...
A study of U.S. colleges and universities resulted in the demand equation q = 20, 000...
Find the total value of the given income stream over the interval 0 ≤ t ≤10...
1- Find the area enclosed by the given curves. Find the area of the region in...
In a 2 sec lab experiment a particle moves in a straight line while its acceleration...
There is gas in the trough and the gas has a density of 2000 ??/?3 ....
Show that there is a solution to the equation e^x=3-2x in the interval(0,1)
6. Let ?(?) be a continuous function defined for all real numbers, with?'(?)=(?−1)2(?−3)3(?−2) and ?''(?) =...
Find the angle, in degrees, between the planes 2x-3y+6z=5 and x-2y+2z=4. Respond the obtuse angle between...
Find the unit tangent vector T and the principal unit normal vector N for the following...
given the following supply and demand functions find the consumer's surplus and producer's surplus. s(x)= 0.09x2...
Find the directional derivative of the given function where (x,y)=(1,1) in the indicated direction Direction <3,4>...
If f(2)=100, what is the value of f(5)?
The base of a solid is the region in the first quadrant bounded by the graph...
Find the minimum and maximum of F(x)=x^3-ax
Use the Chain Rule to find the indicated partial derivatives. P = sqrt(u2 + v2 +...
1. Use a definition of a Taylor polynomial to find the Taylor polynomial T2(x) for f(x)...
Use shell method to find the volume of the solid generated by revolving the region bounded...
Given the function f(x)=−2+x^2, calculate the following values: f(x+1) ; f(x)+f(-4)
The altitude of a triangle is increasing at a rate of 1 cm/min while the area...
1. Evaluate the limit using L'Hospital's rule if necessary lim x→∞ (1+ 12 / x)^x/1 2....
Find the quadratic approximation (Taylor Polynomial) for f(x,y) = 2xe^(2y) near (2,0).
A furniture store sells two styles of a chair, reclining and non-reclining. During the month of...
Suppose that over a certain region of space the electrical potential V is given by the...
if F(x,y)=2xyi+(x^2+2y)j , find the work done by compute fc(F) *dr , where C is an...
A trough is 4 feet long and 11 foot high. The vertical cross-section of the trough...
Find the absolute maximum and minimum values of f on the set D. f(x,y)=2x^3 +y^4 +2,...
Find the curvature of the curve r(t)= < et , t , t2 >.
I am having trouble simplifying this question as most of my examples are different than this....
Find the global maximum and global minimum of f(x, y) = y^2 +xy −x^2 on the...
Find an equation for the line tangent to the curve at the point defined by the...
Let Y = 3x2 + 12 x find Y` ____0____ Find the critical point(s) for Y`...
Find the total flux of F = −xi−yj + (z^2)k through the portion S of the...
Let C ⊂R3 be the parametrized curve X(t) = (√2t, (2/3)t^(3/2), (2/3)t^(3/2) ), t ∈ [0,1]....
Calculate ∬Se^(−z)dS where S is the surface given by x2+y2=4, 0≤z≤7.
A swimming pool is 50 ft wide and 100 ft long and its bottom is an...
Set up a double integral to find the flux of the vector field F = <−x,...
6) Given y = [ e ^ (2x+1) ] / [2 ^ (1 - 3x)], then...
1a) Evaluate the limit as x goes to infinity using l'hopitals rule (x^-1/3)/sin(1/x) 1b) Evaluate the...
Let f(x)=6x^2−2x^4. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates...
Given two planes in space: 2? − ? + 6? = −4 and 5? + 3?...
calculate ∫ sin^2 (wt) dt
2. Where H iis the patient’s height in cm, w is the patient’s weight in kg,...
Find the curvature of the path and determine the tangential and the normal components of acceleration...
given the plane P:2y-3z-6=0, find scalar parametric equations for the line perpendicular to P that passes...
Find the distance between the skew lines L1: x = 1 − t , y =...
Evaluate lim x→0 ((x + 4)^3/2 + e^x −9) / x , without using L’ Hospital’s...
Find the point of intersection of the lines (x-2) / - 3 = (y-2) / 6...
Find the indicated maximum or minimum value of f subject to the given constraint. Maximum: f(x,y,z)...
Find the volume of the solid generated by revolving the region bounded by y = 2ex...
integral of sin^2(3x)cos^4(3x)
Find a formula for a curve of the form y = e − ( x −...
Find the slope of the tangent line to the curve r = sinΘ + cosΘ at...
Hi, please solve this below antiderivatives ( integration) questions. Thanks Find the antiderivative using proper symbolism...
Find parametric equations of the line that passes through (1, 2, 3) and is parallel to...
Explain the concept of linearization and why we use this. I get that linearization is the...
1. Let f(x)=x^2−4x+3/x^2+2X-3 Calculate lim x→1 f(x) by first finding a continuous function which is equal...
Find the area to. A. The area below the curve ? = 3(1) + ??^x in...
Consider the surface given by the part of the plane z=y+3 that lies inside the cylinder...
Find the relative maximum value of f(x,y)=x2-9y2, subject to the constraint x-y=24 The relative maximum value...
What is the binomial expansion? in context I am trying to get the maclaurin series for...
Find the mass and center of mass of the lamina that occupies the region D and...
If the minimum velocity is 30 feet per second, initially measured at ? = 0 seconds...
Let f (x) = e ^6/x^6 . Find a simplified expression for f ′′(x).
Find the curl and the divergence of the vector field. ?(?,?,?) = 2?^2? + (4?y +...
Plot the point whose spherical coordinates are given. Then find the rectangular coordinates of the point....
Find the Sum of a Convergent Series: a.) ∑∞?=0 (-4/9)n b.) ∑∞?=0 1/(n+1)(n+4)
water is leaking out of an inverted conical tank at a rate of 8900.0 cm^3/min at...
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