Consider the function f (x) = x(Va – 1), where a > 0, x > 0. If 0 < a < 1, show that limx0f (x) is a negative number.

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: Graph g(x) = x sin (1/x) to estimate limx→0 g(x), zooming in on the origin as necessary. b. Confirm…

A:

Q: Find the limit, if it exists.

A: Here given as

Q: Plot the function and use the graph to estimate the value. lim 2x − cos x/xx→0

A: Given:

Q: Use the following definition of a derivative fla=lim f\x-f(a) x-- a x-a To find fa), where f x=x°-…

A: Given, f(x)=x3-2x  To find f'(a).  Solution: f'(a)=limx→af(x)-f(a)x-a      =f(a)-f(a)a-a=00

Q: Find the value of the limit lim SINX X 0 2x 02x (a) 0 (b) 1 (c) 1/3 (d) 1/2 (e) 1/4

A: Here we have to find the limit of the function. In the first step use the property of the limit:

Q: 2. Use a table of function values to estimate lim in3x sin 3x sin3x -0.1 0.1 -0.01 b. 0.01 -0.001 c.…

A:

Q: Find Lim as x approaches 0 of the function cos(4x-1)/2x

A: Given: limx→0cos4x-12x To find:  The limit limx→0cos4x-12x

Q: Find the limit. 1+x? lim arccos 1+ 2x2

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

Q: Find the limit. lim (1+ sin(3x))/* x→0+

A: Given: u=(1+sin(3x))1x We want to find  limx→0+u=limx→0+(1+sin(3x))1x Since we know that u=eln(u)…

Q: lim 4 sin(x + n) + 3

A:

Q: Evaluate the limit.

A: We have to evaluate the following limits- limh→0sin4h4h

Q: Evaluate the limit: sin(5x) cos(6x). lim x→0

A:

Q: Find the limits limx→q(ln x)1/x

A: Given,     limx→qln x1x

Q: lim (sin?x x-0 x2

A: We use L-Hospital Rule to evaluate this limit.

Q: Evaluate the limit: sinx lim x→0 e4x – 1

A:

Q: Find the limits in Exercise

A: Given,

Q: 1-cos 2x lim X→0 x2

A: Hello! thank you for the question but as per our honor code, we'll able to solve only the first…

Q: sin²t lim t3 t→0

A:

Q: Evalute the lim sin5x/x(x-1) as x approaches 0.

A:

Q: Evaluate the limit. lim     In (Sinh x)x →0+

A: we have to evaluate the limit. lim     In (Sinh x)x →0+

Q: Determine the value of the following limit. sinh(x) = x lim - x3

A: Given that limx-&gt;0 sinhx-xx3

Q: . Use the sandwich theorem sin x (a) lim Vx 400

A: The given expression is: limx→∞sin xx

Q: Use the Squeeze Theorem to prove lim = 0. x00 x+ e- For x 0, since 0 < e* <1, we have

A:

Q: Determine the 2.x2 – 4x + 6 dx using the definition. (hint: lim Rn)

A: Given: ∫12 2x2-4x+6 dx  To find: Value of the limit.

Q: (a) Evaluate the following limit: lim ) (1-e3x x²+3x, x-0 (b) Find the equation of the tangent to…

A:

Q: find the limit. lim x→∞ e-x (sin x)

A:

Q: Evaluate the limit.

A: We have to evaluate the limit: limh→0sin 9hh We know that limx→0sin xx=1 So making same angle of…

Q: For f(x)=√7x+2, find f′(x) using the definition f′(x)=limh→0f(x+h)−f(x)/h. f′(x)= Using this, find…

A: Equation of the line passing through the points x1,y1 and having slope m is y-y1 =mx-x1.

Q: Find the limit, if it exists. lim X 00 4X + sin x 2.

A: Our aim is to find the limit of the following:limx→∞  24x+sinx  = ?

Q: Consider the function: f (x) · g (x) = 16x · sin What is lim f (x) · g (x)?

A:

Q: If [ f(x)\dx<∞ show that limf(x)dx=0 k→∞00 1

A: We have to prove that given expression.

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: lim cos x*/x x→0

A: Given,          limx→0cosx1x

Q: Find the limit. lim est - 1 t-0 sin(t)

A:

Q: - Find the Lim;t: O Lim Sinx メー0 12ナメ3 E. 4) Lm sint2 sino lim 下-日

A:

Q: Find lim 2x sin using the Squeeze theorem. x-0

A:

Q: Use numerical evidence to estimate the value of the limit to at least 2 decimal places. - x – 20 lim…

A: Here we have to evaluate the limit of given function

Q: Find the limit, if it exists.

A: First of all, use the limits property and apply the limits on numerator and denominator.

Q: Estimate the limit numerically or state that the limit does not exist (DNE): sin(9x) lim x →0

A: Please refer the attached image for complete solution. THANK YOU.

Q: Find the limit: 1 – cos(x) lim x2

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: For f(x) = 2x³ - 2, find ƒ '(x) using the definition f '(x) = lim f(x+h)-f(x) h h→0 f'(x) = Using…

A: Let's find.

Q: Find the limit. lim sin-2x i

A:

Q: Evaluate the limit sin 2x lim z+0 9x

A: Answer and explanation is given below

Q: Find the limit by interpreting the expression as an appropriate derivative. e2x lim- 1 i X0

A: As we already know that, dydxx=a=limh→0f(a+h)-f(a)h

Q: Find the limit. lim X→- 47 Vx+ 15 cos (x+ 4x)

A:

Q: Compute the limit below. Justify your answer. sin(24x) lim- 39x

A:

Q: Compute the lim as x goes to 0+ (e^x - 1 - x)/ (xe^x - x)

A: we have to compute the limx→0+ex-1-xxex-x

Q: If f' is continuous on [0, ∞) and limx→∞ f (x) = 0 , showthat

A: Given, If f' is continuous on the interval [0,∞) and limx→∞f(x)=0 show that, ∫0∞f'(x)dx=-f(0)