SEvaluate the limit by rationalizing the numerator. V4+t- V4-t lim t>0 3 (b) lim | t 9+t

Q: Find the slope of the function's graph at the given point. 8 Function: g(x) Point of g is at (10, 0....

A:

Q: 2. I t/Cos X SinX

A:

Q: Find the maximum rate of change of f(x, y, z) = x + y/z at the point (1, 1, -5) and the direction in...

A: We have to find the maximum rate of change

Q: A necessary and sufficient condition that M(x,y) dx+N(x,y)dy=0 be a homogeneous equation is А M and ...

A: Here we have to find which condition satisfy that the given differential equation will becomes homog...

Q: 1. If ü= (2,-3), v=(1, -5), and w=(6, 2), determine the following: a) |ü +v| b) 3 ỹ -ū +w

A: a) u→+v→=(2,-3)+(1,-5)=2+1,-3-5=3,-8=32+(-8)2=9+64=73|u→+v→|=73

Q: 3.fCx)3D63X²4X+2 x<1 2x-1 X71 Part A: IS f(X) lontinuous ar X-1? JustfY answer. Palt B)EXPainunyfeX)...

A:

Q: (a) f(x) =x² – 2r

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: Graph each: 1. f(x)= sin(2x)-2 Amplitude: %D f(x) Period: Vertical Shift:. Phase Shift Start: End: I...

A:

Q: Find dy/dx: (a). y = cos 8x + sin r2, (b). y = Vcos 8x + sin x². %3D

A:

Q: The given function is not one-to-one. 9(x) = (x- 3)2 y 10 -10 -5 10 -5 -10 Restrict its domain so th...

A:

Q: 3.) y tanʼxdx +ln* ydy = 0 dy_ (y?+4) Inx In (y?+4)Y 5) dx

A: y tan2x  dx + ln4y dy = 0∫-tan2x  dx =∫ ln4yy dy∫(1 - sec2x) dx  = ∫ t4 dt   (where, t = ln y)Hence,...

Q: Find the curvature κ of r(t) = at t = 0. Simplify your answer

A: use curvature formula for vector valued function.

Q: ОА. (х+82 + (у - 9)2 3 9 О В. (х+9)2 + (у -8)2 %3 3 OC. (x-9)2 + (y + 8)2 = 3 O D. (x-8)2 + (y + 9)²...

A:

Q: Express the repeating decimal as a fraction. 5.919191...

A:

Q: Let f(x, y, z) = xy° + zª and æ st, y = st, and z = s't. (a) Calculate the primary derivatives

A:

Q: 1. f(x)=3sin(2x-180")-2 Amplitude: f(x) Period: Vertical Shift. Phase Shift Start, End. Increments,

A:

Q: f(t) = 16t2 + 330t + 6. %3D ... What is the height of the ball at 4.6 seconds? ft.

A: SOLUTION-

Q: For the curve given by r(t) (-4t, 6t, 1 – 7t2), Find the derivative '(t) = ( -4 6 -14t Find the seco...

A:

Q: Use the matrices below to perform matrix multiplication. 5 10 4 C -10 0 12. 3 6 B -2 7 6. 8 If the o...

A:

Q: Consider the graph of 7x2 4x + 4y? – 5y = 100. - - - 4x + 4y? – 5y If the graph of 7x? stretched hor...

A: Topic:- calculus

Q: First make a substitution and then use integration by parts to evaluate the integral. (Use C for the...

A: The given integration,        ∫arcsinlnxxdx

Q: Which of the following uses integration by parts? (3) fxlnxcx In x dx ... (1) fxcosx'dx (2) fre*dx A...

A:

Q: f(x)=7+2x−2x^2, find the equation of the line tangent to the curve f(x)

A:

Q: World population' is about P = 7.68(1.0103)', with P in billions and tin years since 2020. (a) What ...

A:

Q: > [2] S 1+e* dx 1-ex

A: The solution is given in the next step.

Q: Let P be the point (4,5,5) and Q be the point (2,5,3). What is the distance between P and Q? You may...

A:

Q: There is an tnfinite discontinulty 10. There is a jump discontinulty at x 0 and f(0) = -2 at x = 1 a...

A: There is an Infinite discontinuity at x=0  and f(0) = -2

Q: For the following exercises, find the lengths of the functions of X over the given interval. If you ...

A:

Q: 4 and y(4) 10, find y'(4) by implicit differentiation. If 2x + 3x + ry

A: We can perform the implicit differentiation to find the answer as below.

Q: Here is the position function for projectile motion on the planet Glorg (gravity is different: g = 1...

A:

Q: Let V u R. It v 1s prpndioulnt be Vectors in to u, then my parpindientar to' u. nonzoco Malhple GU o...

A: topic - vectors

Q: The following series converges. Compute the sum. 3. 2e()" n=2

A: The given series,        ∑n=2∞2e3πn

Q: WHIK the eqation tor the planc thronh Pont to ne -Bi -でiroh 水e5 and nomal

A:

Q: Determine the equation of the tangent of the function, f(x) = 4−x / x+2 at x = 2.

A: According to question,Given function,fx = 4-xx+2

Q: Differentiate. t2 y = 8t2 - 2t + 1 dy dt

A: topic - derivative of the function

Q: 2 dse the Reimann Integral to evaluate S v'dv.

A:

Q: 3. f(x)=2cos(x-90°)+1 Amplitude: f(x) Period: Vertical Shift: Phase Shift Start: End: Increments:

A: Topic:-  function

Q: Consider the given system. 2x + y == 0 Graph the inequalities on your graphing calculator, and fin...

A:

Q: 12x + 13x2 lim 13x3 - 7

A: limx→∞12x3+13x213x3-7=limx→∞x3(12+13x2x3)x3(13-7x3)=limx→∞(12+13x)(13-7x3)=(12+0)(13-0)=1213

Q: Choose the correct graph of y = cos x, -T< x< T: 37 2

A: Given the query is find the graph of the cos function.

Q: Show every details of your solution, so it would help me to understand on how it become. I NEED A VE...

A:

Q: (1) In this question we will find a recursive formula for the integral | (In z)" dr. In (n) Find I1 ...

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

Q: Differentiate the following function. 1 v = t8 - %3D v' =

A: We have to find derivative

Q: 3. Given the polar curves r = 1- 2 sin e and r = -4 sin 0. Do the following: a. Sketch the curves on...

A: see below the answer with the help of the graph of the function we will find the value of the angle ...

Q: The monthly revenue R (in dollars) of a telephone polling service is related to the number x of comp...

A:

Q: Perform the indicated integrations. 1. S- ydy 25-16y 2. zdx 9+x2 dx 3. Jax-4x+5

A: since you have posted multiple question i can do first three question as per our company guidelines....

Q: (+++)" В. y C. y = 2x/x² + I

A:

Q: 2 f(x)=-3cos(x+45")+1 Amplitude: %3D f(x) Period: Vertical Shift: Phase Shift Start: End: Increments...

A: solution given below

Q: To evaluate: The integral function x2 +x + 1 -dx. (x² + 1)²

A:

Q: The length function for the curve yz ln(sinx) arc stacting point (,0) cwith

A: The arc-length of the curve y=f(x), a≤x≤b is given by: L=∫ab1+(f'(x))2dx