Find the following: i. Lim →x/+9x/6x/−4x/ ii. Lim →(2x−1)/−3x−5

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A: The given function is To prove

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A: We have to calculate the limit

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Q: Find the following: x1/3 + 9x1/5 i. Lim x-0 6x1/2 – 4x1/4

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A: The given limit is: limx→0-2lncosxx2   As we know that; The Chain rule: fgx'=f'gx·g'x

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A: Consider the given limits

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A: To evaluate the given limit.

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A: The objective is to evaluate the limit.

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A: We can find the limit as below.

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Q: Find the following: x1/3 + 9x1/5 (2х — 1)1/2 — 3 - i. Lim 6x1/2 – 4x1/4 ii. Lim x→5+ х — 5

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Q: lim х-2 x→2 Vx + 7 - 3 Score С. 1 А. 6 В. 4 С. 2 D. 0

A: As we can observe that it is an indeterminate form(0/0). To solve the limit, multiply and divide the…

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Q: find the limit or explain why it does not exist

A: Part (a) limx→0x2-4x+4x3+5x2-14x=limx→0x2-4x+4xx2+5x-14=limx→0x-22xx-2x+7=limx→0x-2xx+7 Now…

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Q: Forf (x) = 2x +2, compute lim ƒ(1+h) –f (1) %3D f(I+h) -f (1) lim h>0 %D h

A: Given : fx = 2x+2

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Q: For the function f(z) = 4x + 19z + 28, find f'(x) using the f(x +h)- f(x) definition lim O 8% O 38z…

A: Here we will find f'(x) using the given definition.

Q: lim. J25x+2sh+6 50 25 x+650 w

A: Given,          limh→025x+25h+650-25x+650h

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: