x' + 2, if x < 0 1. Suppose f(r) = %3D |x – 2|, if x > 0 (a) Find lim f(x).

Q: Find the limit of sin(6x) limy→0° sin(2x)

A:

Q: find the limit as x approaches 1 from the right of  ln(x^9-1)-ln(x^7-1) using L'Hospitals' rule

A:

Q: 5 Find a limit equal to In(2x – 1) dx.

A: We know that, ∫lnxdx=xlnx-x+C…

Q: why is the limit as x approaches 0 equal to 1/5 in the equation: ((sinx)/(5x))

A: The given limit is,

Q: lim at e -

A: Find the limit when x tends to 0

Q: limit x approaches 0, (xcot2x)

A: Limit x-&gt; 0 ( x/tanx ) =1Calculating the limit of the given expression using this result:

Q: lim sin (-2 T x) = x → -3

A:

Q: Limit as x approaches 0 1-cos(x)/sin(x)

A:

Q: TX-1 t. Lim ×つ○ 1

A: limx→0 πx-12x2    +πx(e2πx-1)=limx→0 πe2πxx-πx-e2πx+1+2πx2x2 (e2πx-1)   limx→0 πx-12x2…

Q: lim b-> -0.1x e 1.

A: Let I=limb→∞∫1be-0.1xdx

Q: lim as x--&gt;0  of (x+1-cosx)/x

A: The given limit of the function:

Q: Find lim (2+x)" * using L'Hôpital's rule. 1/x

A: Given the given expression is limx→∞2+x1x.

Q: Find the length of the graph of f(x) = ln sec x from x = 0 to x = r/6.

A:

Q: Find the limit of * sin(6x) limx→0 sin(2x)

A: Given problem is :

Q: 1 () X. lim х+ sin X→+∞

A: The objective of the question is evaluate the limit of the given function.

Q: sin(x – 3) lim X→3 + 6x – 27

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: A tank contains 1720 L of pure water. Solution that contains 0.06 kg of sugar per liter enters the…

A:

Q: x-sinx 1. lim X-0 x-tanx

A: Given function is limx→0x-sinxx-tanx

Q: Suppose g(x)=4x^2-lnx is the derivative of f(x). Compute Lim x->0 (f(x+1)-f(1)/x) Please show steps…

A:

Q: Calculate the limit for the function f(x) = Ex + 4 over the interval [0, 4]. Verify your answer by…

A: Given the function

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 length of the arc of f(x) = ÷ (1+ x²)ē between x = 0 and x = 3. %3!

A:

Q: limit of (x + 5) as x approaches to 3 po yung given if ever blurred. ty!

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: ) A tank contains 1700 L of pure water. Solution that contains 0.04 kg of sugar per liter enters the…

A:

Q: cosx * sin? (3x) 2 2. lim x→0 x2

A:

Q: (sin 2x)* - 4x →0+ x -

A:

Q: Question 5- Evaluate the limit. Vx-1 lim Question 6 - Find the equation of the tangent line to y = -…

A:

Q: According to the alternate form of the definition of the derivative, to compute f′(0), we need to…

A:

Q: 6x +55 –5 lim X +5 x+ -5

A:

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

A:

Q: lim(cos' x+sin 5x) tan 3x x→0

A: Given- limx→0cos3x+sin5x2tan3x To Find- The value of the above limit.

Q: Find the limit.   Lim x→∞             (1+2x)5/2 ln x

A:

Q: Find the limit. lim x→4  sin(x − 4) x2 + 5x − 36

A: To Determine: find the limit of  limx→4sin(x-4)x2+5x-36 Given: welimx→4sin(x-4)x2+5x-36 Explanation:…

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

A:

Q: Evaluate sin(x – 3) - lim x→3 x2 + 1x – 12 Limit = (Enter DNE if the limit doesn't exist)

A:

Q: Express the limit as a definite integral on the given interval. lim [9(x;)³ – 9x;14x, [2, 8] i = 1…

A:

Q: Compute limx→0 sin(x) − x divided by  x^3

A: We have to evaluate the limit: limx→0sinx-xx3 After putting limit value we can see that this is 00…

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

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

Q: Find the limit of sec x as x approaches x lim sec x x->0

A: Topic = Limits

Q: limit x to infinty tan(5t)sec(99t)/t

A: Lim           f∞(st) Sec(q q t )tx→∞    Here limit x→∞ But the function is in t ∴

Q: Evaluate the limit: sinh x2 – x2 lim x→0 sinhx − x

A:

Q: Calculate the limiting value for 1 cos(x*) – 1+5x³ lim x→0 х16

A:

Q: Find the limits limx→0+sin x . ln x

A: The given limit is: limx→0+sinx·lnx  Consider "h" is a too small positive real number,  Then,…

Q: limit x approaches zero, sin^2x/x

A: Given,

Q: 1 lim, „(e* + x)÷ +00

A: Explained below

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: