Compute the limit as xà0 of f(x)=(sin(61x))/x, if possible.

Q: Evaluate the limit using L 'Hospital's rule: lim x to 0 e^x -1/sin(12x)

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Q: For the function given by q (x)= x² + 2x+1, use the limit definition of the derivative to compute…

A: Definition of the Derivative:        The derivative of f(x)  with respect to x is the function f'(x)…

Q: Find the limit. sinx cos 4x lim x-0 x + x cos 5x 4 A) 을 B) 0 530 C) D) Does not exist

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Q: Find the limit, if it exists.

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Q: Evaluate the limit sin x/x as x approaches 0 when x = -1

A: We have to evaluate

Q: 4. Does f(x) = : (0, 00) → R have a right limit at x = 0? If yes, compute the limit. If not, explain…

A: We need to calculate when x->o+ from right side then f(x) exist or not.

Q: Use L'H to find the limit at x \arrow 0: arctan(5x)/x   x-->0

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

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

Q: Compute the limit as x approaches infinity of x^e-x

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Q: What is the limit as x goes to 0 for (e^x-1-x)/x^2?

A: Please refer the attached image for complete solution.

Q: express the limit as a derivative.

A: Given expression

Q: What is the limit of (e^x-e^-x)/( sin (x)) as x approaches 0?

A: we have find the value of limx→0ex-e-xsin x

Q: evaluate the limit  limit as x approaches infinity of x+cos(x)/ x+1

A: To find,

Q: Express the limit as a definite integral on the given interval. lim n - 00 cos(x}) Дх, [2л, 5л] Xi i…

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

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Q: what is the limit of (cos(x))^4/x^2 as x approaches 0 from the positive side?

A: Given,

Q: Compute the limit as x goes to 0 of [tan(x) - sin(3x)] / (x^2)

A: limx→0[tan(x)-sin(3x)]x2=[tan(0)-sin(3(0))]02=00

Q: 1 is equal to cOs x - The value of the limit lim x2

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Q: Evaluate the limitlimx→0+x sin(x) + x^2/ x^2

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Q: 2. Compute xe" da using a limit.

A: The given which we have to find the integration from 0 to ♾️  f(x) = xex

Q: if f(z) = V3+ 3z, find f'(3), using the definition of derivative f'(3) is the limit as z+ of the…

A: Given query is to find the derivative using definition.

Q: Evoluate the limit of (1-cosx) (x²) as x pproaches 0.

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Q: given f(x) = (2x+1)/(x+3), use the limit definition to find the tangent line to graph of f(x) at x=0

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Q: compute limit as x goes to 0 of (sin(x)-x)/(x^3)

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Q: Find the limit, if it exists. sin(4x) x Ilm

A: To find the following limit, if it exists.limx→∞ sin 4xx

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

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

Q: Find the limit of xsinx as x approaches 0

A: Given:

Q: Evaluate the​ limit, where a and b are constants with b≠0. lim x -0 sin ax/ sin bx

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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: Find a value of the constant k such that the limit exists.

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Q: Estimate the limit numerically or state that the limit doES not exist (DNE): sin(9r) lim

A: Evaluate: limx→0 sin9xx

Q: Find the limit by interpreting the expression as an appropriate derivative. In (e10 + Дӕ) — 10 (а)…

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Q: Express the limit lim,, +00 Ei-1 8i2 as a definite integral.

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Q: Find the limit as x approaches 0  2sin23x/3x2

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Q: Given f(x) = 5VI + 1, find f'(x) using the limit definition of the derivative. f'(x)-|

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Q: Find the limit of tan^-1(e^(x^2)+x^2+1/x) as x approaches negative infinity

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

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Q: Find the limit limx→0ln(1+4x)sin3x.

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Q: lim,0+ ((sinx)tan

A: Given function is limx→0+sin xtan x. To find: Limit of the given function.

Q: Find: a. f (0) b. limit of f (x) as x approaches 2 from the left c. limit of f (x) as x…

A: We have to find

Q: (b) lim log1 r+2+ (x – 2)? sin(2x2 – 3x – 2),

A: solution:-limx→2+ log13x-22sin2x2-3x-2=limx→2+ -log3x-22sin2x2-3x-2=limx→2+…

Q: find the limit as x goes to infinity of ln(x+1/x+2)

A: Evaluate the limit

Q: Does the existence and value of the limit of a function f(x) as x approaches a ever depend on what…

A: Yes, existence and value of the limit of a function f(x) as x approaches a depends on what happens…

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

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Q: Find the limit. (e-sx cos(^) lim X- 00

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Q: Find the limit of (x3+x2)1/2sin(((2)1/2pi)/x) as x approaches 0

A: To find

Q: Express the limit as a definite integral on the given interval. lim [9(x*)³ - 2x*JAx, [2, 9]

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Q: Find the limit for the following functions: x-sinx 1-lim, x-Vx² + 2x 2- lim,-o

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