Evaluate the limit. (If an answer does not exist, enter DNE.) y= lim (10x)$sin(7x) X0+ %3= Work must include natural logs, all steps necessary in evaluating the limit, including any derivatives taken, and you must clearly label each time L'Hopitals is used.

Q: Verify that L’Hôpital’s Rule applies and evaluate the limit.

A:

Q: The limit used to find the derivative is f(t) – f(x) dy dx lim definition %3D t- x

A:

Q: Let S-6x2 + 6z for z 0. According to the alternate form of the definition of the derivative, to…

A:

Q: A tank contains 1900 L of pure water. Solution that contains 0.02 kg of sugar per liter enters the…

A:

Q: Find the slope of the tangent line to the parabola y=4x-x^2 at the point (1,3) 1) using the…

A: Given

Q: Find the limits. Are the functions continuous at thepoint being approached? lim x →1 cos-1 (ln √x)

A: We find the limit by substitution

Q: Approximate the given limit numerically and verify your answer graphically. Round your answer to…

A: Given limit, limx→0+xlnx+x2

Q: Find the limit. y sin x limx.y)(0,1) O 1 8. O No Limit

A: Find the limit. lim (x.y)→(0,1) (y5 sin x)/x To select correct option  1 0 ∞ No Limit

Q: 1) For the function f whose graeh is given the value of each lihmit. If a limit dosent exise enter…

A: From the given graph :

Q: Based on the given values, is the function continuous or not? If not, select the condition which is…

A: In the given question we have to tell such function which satisfies the given three property and and…

Q: Show that r sin (1/x) fails to have a derivative at r = 0 and even the one-sided limits (lim,-0+ (f…

A: We will prove the given statement.

Q: find the limit. limit as x approaches 0 sin23x/x2

A: Apply the limits and find the in-determinate form.

Q: Suppose that f(x) is a differentiable function (with a continuous derivative), such that f(0)=…

A: To obtain the value of limx→03x-fx4x-fx, substitute 0 for x and 1 for f(0) in the expression, and…

Q: • If you are asked to find z- or yvalues, enter either a number or a list of numbers separated by…

A:

Q: Find the limit of the given functions using a numerical approach 3. lim (2 cos x) 3T 4.

A: The solution of the problem is given in the next step.

Q: sin xy lim 0.

A:

Q: express the limit as a derivative.

A: Given expression

Q: Find the derivative of the function by the limit process. h(s) = −2 (square root of x)

A:

Q: Find the limit of the transcendental function. lim x → T/2 4 sin x

A: Definition of limits helps to find the limit of the given function. The value is said to be the…

Q: Computing the derivative of ƒ(x) = x2 ex

A: Consider the given function fx=x2ex

Q: find the limit. limit as x approaches 0  sin4x/sin6x

A:

Q: If lim f"(x) = +00, then the trapezoid estimation Tn - f(x) dx O TRUE OFALSE can never be within…

A: Given,

Q: 9. Build a table to estimate lim sin (Hint: Use multiples of T) X-0

A: Given: To Find:   A table to estimate the value for the given function.

Q: Discuss the relationsh ip between the derivative dy/dx and(lim) with drawing if it is required

A: See the attachment

Q: 1. To take the derivative of the following function. х т (1) y = m (2) y = x' log 2. To find out the…

A:

Q: 4. Find the differentiation dy. using definition with limit of the following: y = V2x + 1.

A:

Q: Q1) A) Find the tangent equation for the function: f(x) = vx2 + 5 at =2 ? B) Find the limits by…

A:

Q: Use logarithmic differentiation to find for y = x4* %3D dx 2x Use LaHopital's rule to calculate the…

A:

Q: Find the limit.  limit as x approaches 0 sin3x/x

A: Apply the limits and find the in-determinant form.

Q: If lim f"(x) = +0o, then the trapezoid estimation Tn - | f(x) dx %3D x0* can never be within 10¯³ of…

A: Given that limx→0+f''(x)=+∞ And Tn≈∫01f(x)dx Error for trapezoidal method contains double…

Q: cosx * sin? (3x) 2 2. lim x→0 x2

A:

Q: E. Set up the limit definition for finding the derivative of y = sin x.

A: Givne that  y=sinx  From the limit definition find the derivative of y=sinx

Q: Make a table of function evaluations near the limit and use this to estimate the value of the limi…

A: Given: f(x)=limx→0xsin)(x)

Q: Suppose that f(x) is a differentiable function (with a continuous derivative), such that f(0)=…

A:

Q: Estimate the limit numerically or state that sec (x) lim x→1+ vx³–1 (Enter DNE if the limit doesn't…

A:

Q: verify that L’Hôpital’s Rule applies and evaluate the limit.

A:

Q: a. Graph h(x) = x2 cos (1/x3) to estimate limx-->0 h(x), zooming in on the origin as necessary.…

A:

Q: x sinh x 1. lim x0 cos 3x -1

A: The solution of the problem is given in the next step.

Q: Find the tangent equation for the function: f(x) = Vx2 +5 at x=2? Find the limits by using L.Hopital…

A:

Q: A tank contains 1980 L of pure water. Solution that contains 0.05 kg of sugar per liter enters the…

A:

Q: a) By graphing the function f(x)=(cos2x-cosx)/x2 and zooming in toward the point where the…

A: Graph: f(x)=cos(2x)-cos xx2f(x)=cos2x-sin2x-cos xx2

Q: suggested that you report answers accurate to at le sin(12a) Let f(æ) = sin(12x) We want to find the…

A:

Q: Find the limit as x approaches negative infinity of (xe1/x-x)

A:

Q: Match the given limit with a derivative. Then find the limit by computing the derivative. lim 49 h-7…

A: Derivative by definition formula is

Q: Evaluate the limit sin 7h lim %3D 7h Enter DNE if the limit does not exist. Limit =

A:

Q: Find the limit sin(3x)cos(4x) lim→0 x+xcos(5x)

A:

Q: 1. Find the points at which f is discontinuous. At each of these points, state the type of…

A: