Can you explain the steps to solving this? 1.8  38) lim x->2   X3 / √x2 + x - 2

Q: a. Find the slope of the tangent to the curve y = 3 + 4x2 - 2x3 at the point where x = a b. Find equ...

A: Given curve is, 

Q: Duule LIUZIJVTU, "Pom Find the values of a and b that make f continuous everywhere. x2 - 4 if x < 2 ...

A: A function f is continuous at x=a if it satisfies the condition,

Q: GRAPHS AND FUNCTIONS Graphing a piecewise-defined function: Problem type 1 Suppose that the function...

A: Given information:The piecewise function is shown below: 

Q: what is the limit of x minus the square root of x, as x approaches infinity

A: Given, 

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x2 lim 3x 40 x5 x 6x5

A: Factor numerator and denominator first. 

Q: For what value of the constant c is the function f continuous on (−∞, ∞)? f(x) =                   ...

A: From the given function it can be observed that it is continuous for all values of x less than 5 and...

Q: How do I solve the limit as x goes to 1 for the expression (sin(3x-3))/(1-x) without using l'hospita...

A: Rewrite the given expression as follows.

Q: can i get help with the problem step by step?

A: We need to find the limit of

Q: 9 Consider the line y=x-4. X Find the equation of the line that is perpendicular to this line and pa...

A: The given equation of line is,

Q: Rewrite the following equations in r and θ as an equivalent equation in x and y; then plot the graph...

A: Rewrite the equation from Polar to Cartesian:

Q: please explain using this theorem, why F(x)= (2x^2 - x - 1) / (x^2 + 1) is continous at every number...

A: consider

Q: Please answer problem 61.

A:

Q: Find the exponential function f(x) = CbX whose graph is given. f(x) _ y (3, 320) (1, 20) X

A: Consider the given exponential function as f(x)=Cbx.The curve of the function passes through the poi...

Q: Snell's Law is an equation from optics which describes how a light ray behaves when it passes from o...

A: The problem concerns formulating an equation for the unknown and applying intermediate theorem to sh...

Q: For problem 11, I have done the proof, but don't know how to interpret the result geometrically. Ple...

A: Since you have asked a very specific query with respect to Q - 11, I will address that query itself....

Q: Write the equation of the circle centered at (−5,10)(-5,10) with radius 13.

A:

Q: Can you help me step by step with this problem?

A: We need to choose the appropriate graph which satisfies the following.

Q: Find the volume V of the described solid S. The base of S is the region enclosed by the parabola  y ...

A: Given base of the solid S enclosed by parabola y=3-2x2 and the x axis and cross-sections are perpend...

Q: Find each x-value at which f is discontinuous and for each x-value, determine whether f is continuou...

A: Find the limit of the function as x approaches 0 from the left.

Q: efined function: Problem type 1 Suppose that the function g is defined as follows. -2 if -2x<-1 if 1...

A: The given function is a piecewise function.

Q: n1 sin(θ1) = n2 sin(θ2),where n1 and n2 are the indices of refraction and θ1 and θ2 are the angles o...

A: Given values are,

Q: The table shows the position of a cyclist t (seconds) 0 1 4 5 0 1.3 5.2 10.6 17.3 24.4 s (meters)

A: Given a table time t(seconds) &amp; distance s(meters).

Q: With initial approximations of x-1 2 and To = 3, V7, correct to at least three significant digits. S...

A: To approximate the value of square root of 7 under the given conditions to the desired accuracy, by ...

Q: Find the area of the parallelogram with vertices A(−3, 0), B(−1, 4), C(6, 3), and D(4, −1).

A: The area of the parallelogram with the vertices is given by,

Q: Suppose that the function g is defined, for all real numbers, as follows. 0 if x1 Graph the function...

A: The function g is defined as,

Q: Use this information to evaluate the following. Hint: do not try to solve for the value of a.     lo...

A: (a)Evaluate the expression loga15 using the given informations as follows. 

Q: With an initial approximation of xo = 3, use Newton's Method to approximate /7, correct to at least ...

A: Concept used: Newton’s Method If xn is an approximation of a solution of f(x)=0 and if f’(xn)≠0 then...

Q: Please draw a handwritten graph of the velocity function with data points.

A: We find rate of changes at every interval first.From x=0 to x=1, i.e. from (0,0) to (1,5) rate of ch...

Q: I know that you need to simplify this so the answer does not become zero but I can't figure out what...

A: Evaluate the given limit in possible case as follows.

Q: 58

A: Given function is

Q: Sketch the graph of an example of a function f that satisfies all of the followingconditions:Range =...

A: It is given that, the range is [–2, 5] and the limit of the function are

Q: I am doing homework for Calculus and I am having trouble with #3 tangent problem on Secction 2.1 of ...

A: The method to find the slope of secant  line PQ is shown on board.

Q: I need help on #29

A: The given integral is

Q: Can you help me step by step with this problem?

A:

Q: Is the function continuous  f(x) = e^x / 1 - e^x

A: We need to check the continuity of the function

Q: Consider the following. x = 3 cos(θ),    y = 4 sin(θ),    −π/2 ≤ θ ≤ π/2 (a) Eliminate the paramet...

A: Calculation:(a)Compute the Cartesian equation as follows.Rewrite the equation x = 3cos(θ)  and y = 4...

Q: question #2 part a correct?  and I dont know how to match these for part b.   Question #3

A: As per norms, the first three questions are answered: Problem concerns derivatives of the given func...

Q: please answer only the questions with the red x's (all of these are subparts of the same question)

A: (a)(ii) The average rate of change with respect to t over [1.5, 2.0] is,

Q: Please answer this questions using the theorems

A: Consider the given rational function as  F(x)=2x2 – x –1/ (x2 +1).Let the numerator and denominator ...

Q: Identify all the types of transformations applied to y=f(x) to yield each of the given equations. Le...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: Find the standard form for the equation of a circle (x−h)2+(y−k)2=r2 with a diameter that has endpoi...

A: Consider the given equation of the circle.

Q: Consider the parametric equations below. x = t2 − 2,    y = 1 − 5t,    −3 ≤ t ≤ 4 (a) Sketch the c...

A: We will make a table for t,x and y. x=t^2-2y=1-5t

Q: 3. Use the given graph of f(x) = vx to find a number 8 such that IVx - 20.4 x48 then if yA y Vr 2.4 ...

A: Consider the second inequality.

Q: Numerator of X2 over denominator of (x-1)2(x+1)=

A: GivenNumerator of x2 over denominator of(x-1)2(x+1)

Q: If 24 J of work are needed to stretch a spring from 15 cm to 19 cm and 40 J are needed to stretch it...

A:

Q: Deposition of partial fractions 5x3+2x-1/x2-1 Can you show me each step to solve this

A: Divide 5x3+2x-1 by x2–1,

Q: Find a parametrization of the circle of radius 5 parallel to the yz-plane with center (-1, 4, 6).

A: The general form of a parametrization of the circle of radius r parallel to yz-plane with center (x0...

Q: Simplify the expressions below. (a) tan(cos−1 x)     (b) sin(tan−1 x)

A: (a)

Q: find f(-x) when f(x)= -3x2+4x-3

A: f(-x)= -3x2 - 4x - 3

Q: Use function notation to describe the way the second variable (DV) depends upon the first variable (...

A: We have been given some description of a relation between two variables in each part of this problem...

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.