f(x) lim, f(x)

Q: What is the displacement of an object that travels at a constant velocity of 10 mi/hr for a half hou...

A: Consider the given information 10mihr for a half hour and  20mihr for a next half hour and 30mihr fo...

Q: Trigonometric substitutions Evaluate the following integrals using trigonometric substitution.

A: The given integral is ∫06z2z2+362dz. Substitute z=6tanθ  and  dz=6sec2θ dθ in the above integral and...

Q: Evaluate the series or state that it diverges.

A: Given: S=∑k=1∞1356k+3579k for evaluating given summation, first we expand given summation so, S=∑k=1...

Q: Given the following y4 + x2y2 +yx4 = y+1 and regard y as independent variable and x as dependent var...

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any s...

Q: Factor trinomial, or state that the trinomial is prime : 9x2 + 5x - 4.

A: 9x2+5x-4

Q: integrate ƒ over the given region. ƒ(s, t) = es ln t over the region in the first quadrant of the st...

A: The given function is fs,t=eslnt over the region in the first quadrantof the st-plane that lies abov...

Q: The intensity of illumination I from a light varies inversely as the square of the distance d from t...

A: The intensity of illumination I from a light varies inversely as the square of the distance d from t...

Q: Find:

A: Apply the limits. limx→1x2+2x-3x-1=12+21-31-1=1+2-30=00   Applying the limits gives 00 form.

Q: Simplify : (x -3) / [x - 3/(x-2)]

A: We have to simplify the expression: x-3x-3x-2 We know that abc=a×cb

Q: Find the inverse matrix, if it exists. (If the inverse does not exist, enter DNE into any cell.) 15 ...

A: The given matrix is A=21518.   The inverse of a matrix A=abcd is given by, A-1=1Ad-b-ca Here, A-1 is...

Q: Use partial fractions to find the indefinite integral ∫ 5 / (x2 + 3x − 4)   dx

A: Evaluate: ∫5x2+3x-4 dx

Q: The given function f(x) = (2x -3)/(x+1) is all one-to-one. For this function, a. Find an equation fo...

A: Given, fx=2x-3x+1

Q: A heat-seeking particle has the property that at any point (x, y) in the plane, it moves in the dire...

A:

Q: How do I solve this?

A:

Q: The graphs show that the three components of love, namely, passion, intimacy, and commitment, progre...

A: Given: The graphs show that the three components of love, namely, passion, intimacy, and commitment,...

Q: Find the general solution of the Following problem? 6y" - y' - y = 0

A: The given differential equation is: 6y'' - y' - y = 0 The characteristic equation is: 6m^2 - m - 1 =...

Q: Find y" if x3 + y3 = 1

A:

Q: Find the areas of the regions enclosed by the lines and curves y = 2 sin x and y = sin 2x, 0≤ x ≤ π

A:

Q: Evaluate and simplify y'. y = 2x Vx - 2x + 2

A: Given,          y=2xx2-2x+2

Q: dx 28. 1– x4

A:

Q: Use the graph (see given herewith) to obtain the graph of the corresponding reciprocal function, sec...

A: Given: The graph of y=12cos2π+x is To determine: The graph of the reciprocal function of the given ...

Q: Use the given acceleration vector and initial conditions to find the velocity and position vector. T...

A: Given equation of acceleration - a(t) = eti-8k                  ................(1)Acceleration is t...

Q: Investigate the family of functions fn(x) = tanh(n sin x)where n is a positive integer. Describe wha...

A: Given: fnx=tanhnsinx To Describe: a. Investigate the family of functionb. Describe what happen to th...

Q: Find the indefinite integrals (most general antiderivatives). You may need to try a solution and the...

A: Let the given integral be y - y = ∫5s+s5ds            .................(1)Integrating equation (1) -...

Q: Find the vertical asymptotes, if any, of the graph of the rational function: h(x) = (x - 1) / (x2 + ...

A: The line x=L is a vertical asymptote of the function y=x−1x2+1, if the limit of the function (one-si...

Q: Insert either <, >, or = to make a true statement. | -20 |   | -50 |

A:

Q: Use the Integral Test or a p-series to determine the convergence or divergence of the series

A: Integral test: Applying integral test we test the convergence of ∫lnxx2dx Integrating this improper ...

Q: Use l’Hôpital’s rule to find the limits

A:

Q: Find general solutions of the differential equation  x^2y'=xy+3y^2

A: Consider the given: x2y'=xy+3y2 Homogenous equation therefore, substitute y=vx and y'=v+xdvdx. v+xdv...

Q: Deriving the Formula for the Area of a Circle Some of the geometric formulas we take for granted tod...

A: According to the guidelines answer to first three parts are given below, please upload other parts s...

Q: How do I solve this?

A:

Q: Use the definition of continuity to determine whether f(x) = (x2 - 9)/(x + 3) is continuous at a= -3...

A: fx=x2-9x+3⇒fx=x-3x+3x+3 The common factor of numerator denominator is x+3. Therefore the given funct...

Q: Solve the equation : x2 + 6x + 1 = 8

A: To solve: x2+6x+1=8 We know that x=±a Therefore, x2+6x+1=8x2+6x+1=±8 Now, solving both equation sepa...

Q: Find the average rate of change of the function:  f(x) = 6x from x1 = 0 to x2 = 4

A: fx=6x Now, f0=60=0 & f4=64=24

Q: Please show all steps

A: Consider the fundamental theorem for calculus 1 using the chain rule. If f(x) is a continuous functi...

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.