e) a) Find all horizon tal and vertical asym ptotes. f(x)- ×2メー_12 2x²+5x -12 (22 Lu(xニ2x)) logx5 b) Find y' for y=

Q: Find the limit of: limit of log5(8x-x4) as x approaches 2- (Use left hand limit)

A:

Q: Find the smallest positive root for the given function by using secant method. S(x) = 4 In(x') – x²…

A:

Q: In Exercises 20–21, find a formula for the derivative using the power rule. Confirm it using…

A: NOTE: Refresh your page if you can't see any equations. . take derivative (using power rule)

Q: Find y" by implicit differentiation. 3x3 + 4y3 = 2

A:

Q: Note that lim (1 - 7x)1/x is indeterminate of type 1°. Using logarithms, we have In(1 – 7x). As x-…

A:

Q: 43. Find the function whose tangent line has slope (x + 1)e¯* for each value of x and whose graph X-…

A:

Q: f(x) = In (3x + e3x)

A:

Q: apply 1rt and second derivative to sketch graph  1)f(x)=3+7e^(-0.2x) and  2)f(x)=ln(2x+4)

A: In the question we have to draw the graph.

Q: By the chain rule, the derivative of arctan (4x^5) is:

A:

Q: In terms of limits, what does it mean for ƒ to grow faster than g as x→ ∞?

A: Suppose we need to find out limits  And f(x) grows faster than g(x), Then denominator gets much…

Q: If - 2x +1 ,when X#! and fcx)= 3 when x= 1 show that The function fex) Continuous at X - 1

A: The detailed solution is as follows below:

Q: Calculate Ls for on the interval

A:

Q: Does the MVT apply to f(x) = - on the interval [1, 4]?

A:

Q: Use the alternate definition, lim Ax)-Aa) to determine the instantaneous rate of X- a change of Ax)…

A:

Q: 2 that also passes Write the equation for a quadratic function f(x) with roots at x = 7 and x =…

A:

Q: If the function is defined y=2x when x=3, is this function differentiable at x=3? Also, is this…

A:

Q: 1 Differentiate f(x) = log, x from the first principle. Note: f'(x) = x In a

A: q- differentiate the function fx=logax from the first principle it is known that, according to first…

Q: 1. If F(x) = - eta dt, find F(1) and F'(x).

A: If Fx=∫exe et2 dt, then to find F1 and F'x.

Q: An object hangs from a string in a stable position and is represented by the function y = 4 sin (3x)…

A: NOTE:Use the form y= asin(bx−c)+d to find the variables used to find the amplitude, period, phase…

Q: Find all the critical numbers for the function g(x) = % xª -- x3 - 5x?

A:

Q: ) Use the limit definition of derivative to compute k'(x).

A:

Q: . Determine the upper bound on the error in the approximation: x2sinx3 x. - if x|<0.8 6.

A:

Q: use graphs to find approximate solutions ex = 4

A: we have to use the graph to find the approximate solution of ex=4.

Q: Find the extreme values of the function f(x)=x√√1- x .- x on the interva

A:

Q: Acrsin a2_v2

A:

Q: 84. Use the definition of the derivative to directly prove thedifferentiation rules for constant and…

A: The definition of derivative states that: f'x=limh→0fx+h-fxh Let the function be fx=c, where c is a…

Q: Find the root between [-1,0] where f (x) = (x+2)' +2x – 5 with error epsilon=0.1 by using False…

A: There are many methods to find the roots of an equation in a given interval. One among such method…

Q: Find the smallest positive root by using fixed-point method f(x) = In(3x)– x² +2 with three…

A: we have f(x)=ln(3x)-x2+2=0 x2=ln(3x)+2x=ln(3x)+2using fixed point iterationxn+1=ln(3xn)+2take…

Q: 5) Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.…

A: The objective is to explain the reason definition of numerical derivative doesn't exist at x=2 in…

Q: What is the maximum point of the function f (x) = x² - x on the o terval [-2,2]?

A:

Q: Show that f(x) =12(logx+1)+x² -10x+3 is a maximum when x=2, a minimum when x=3;

A:

Q: Compute for the derivative of the function f(x)= Arctan (csc2 (3x2/3))

A: Some derivative formulas: ddxtan-1x=11+x2 ddxcscx=-cotx cscx Chain rule of derivative:…

Q: Find y" by implicit differentiation. 4x3 + 5y3 = 6 У" :

A:

Q: Determine the open interval(s) in which f(x) = 2x3 – 6x² is increasing or decreasing. Also, ocate…

A: Given        fx=2x3-6x2

Q: 1.) If the ball IS Thrown. vertically upward with a veloorty of 15 m/s then ts height after t…

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

Q: Find the derivative by the limit process. f(x) = 11-x²

A:

Q: Graph the function y =x + 1                                      x2+1 by applying the first and…

A:

Q: Find y double prime by implicit differentiation8x^2+y^2=4

A: We have given

Q: What is the derivative of the exponential function a x, a &gt;0 and a ≠ 1? What is the geometric…

A: The derivative of the exponential function ax is as follows.

Q: Find y'' by implicit differentiation 4x3+3y3=6

A:

Q: estimate the Root for fox) = X-sinvx USing Simple Fixed Point Iteration with Xo = 1, Es = 17

A: Given that fx=x-sinx, x0=1 and εs=1% The objectie is to find the root using simple fixed-point…

Q: Find the absolute maximum value on (0, oo) for f(x)37-4x--

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Determine the interval(s) on which f(x)=square root(x/x-4) is continuous.

A: Given query is to find the interval where function is continuous.

Q: Find the solution to the equation 2x² - 4x + 1 = 0 using simpsons rule with an lower a and upper…

A: Given , f(x)=2x3-4x+1 we have to use Simpsons rule to find solution with lower limit is 1 and upper…

Q: Solve for the derivative of the function using chain rule. 6. f(x)= cot(6x3+5)

A: Derivative

Q: s(w) = In( w - %3D

A:

Q: Find the orthogonal trajectories of the functen X + ce-X which is . passing Thieugh (-2.0)

A: We need to find the orthogonal trajectories of the function y=x+ce-x, which is passing through (-2,…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.