dy Use the formula dx Ay lim f (x + Ax) – f(x) lim - Ax→0 Ax Ax dy when y = dx 1 to find x + 5 dy dx

Q: If V 16x <f(x)sx+4 for all positive x-values, then what is lim f(x)?

A:

Q: Q3) Using the definition, lim f(k+h)+f(k) h-0 ds calculate the derivatives dk h of the function : k…

A:

Q: Prove that

A:

Q: (a) Find the exact value of the overshoot lim E 1/1- dx/x?

A: Given limn→∞∑j=1n1/j2-∫1πdxx2

Q: Find the limit. lim e 3t i е j + Sin2 tan(5t) k) t 0

A: The given expression is,

Q: For f(x) = 3x*, find using the definition, dx dy Ay f(x + Ax) - f(x) lim Ax-0 Ax lim dx Ar-0 Ax (a)…

A: Given:- f(x) =3x4  To find:-  Using definition of derivative find dy/dx

Q: Find the limit. t2 j+ sin(7t) k sin2(t) -2t ¡ + lim t→0 e

A: We have to find the limit: limt→0e-2t i+t2sin2t j+sin(7t) k

Q: Let y(t) be a solution of ý = y(1 – ) such that y(0) = 6. Determine lim y(t) without finding y(1)…

A: Now,

Q: Express the limit as a definite integral. n 7 lim 8 1 + i = 1 n- o n dx

A:

Q: Find the limit. O 75 π O O' O O I 00 D8 - 150 lim sin¹. 5 x X→ 0 ¹7x

A:

Q: Show that lim (2,v)>(0,0) **+y D0.

A:

Q: Find the Limits: sin (X'ty(0,0)

A:

Q: Use l’Hôpital’s rule to find the limits

A: We have to find the limits of the function by L'Hospital's rule: limt→∞et+t2et-t If we limits are in…

Q: 2x + 1 If t(x) find lim,-o t(x) %3D 8x + 1

A:

Q: Find the limit as x approaches c of the average rate of change of the following function from c to…

A:

Q: is lim x = inf (xn) as x, y. What Express answer and = 3n lim sup (xn) where Xn = [(-1)³ ]+2?

A:

Q: (-cx² + 2x, (sin x + cos x, x> n x<π 9) Prove that lim (x* sin+5) = 5 10) f(x) = What value must c…

A:

Q: dy :) For f(x) = 8x², find using the definition, dx dy Ay = lim Ax-0 Ax f(x + Ax) – f(x) = lim Ax0…

A:

Q: Hi, can I please have this problem solved? Thank you!

A:

Q: Let y(t) be a solution of ý = y(1 - ;) such that y(0) = 4. Determine lim y(t) without finding y(t)…

A: Given that y(t) is the solution of y.=12y(1-y2)with y(0)=4To find the limitlimt→∞y(t)

Q: It can be shown that lim be¯b = 0. Use this fact to compute S*xe* dx.

A: Given: ∫1∞xe-xdx

Q: Find the limit, if it exists, or type DNE if it does not exist. (x + 18y)2 А. lim DNE (x,4)→(0,0) x²…

A:

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

A:

Q: If ƒ' is continuous on [0, ∞) and lim→∞ f(x) = 0, show that I p'(x) dx = = -f(0)

A: First we will integrate then put limit

Q: Along the path x = e find lim (1,y)→(1,0) y2-6ry 3x-y-3 O 2 O does not exist O -3 O 3

A:

Q: OF# Usc the L'Hospital's Rule to compute the limits: B) lim x+5 B00 2x+5* A) lim log, (1+ 2x+x?) and…

A:

Q: 1. Use the delta method, 2 BONUS MARKS y = 5x² dy dx = lim h-0 f(x+h)-f(x) h to find dx for the…

A:

Q: at x sin- 1 lim e J1 x→1 In x " 2 dt =?

A:

Q: dy For f(x) = , find dx using the definition, 19x dy f (x + Δx)- f(x) Ay = lim Ax-0 Ax = lim dx Ax→0…

A: The derivative represents the rate of change of a variable y with respect to x. This implies for…

Q: compute dy/dx using the limit definition.

A: Plug the given equation in the limit definition

Q: nd the limit: lim (e-3t i+ j+cos 2t k) sin2t

A: We have to find limit

Q: Find the limit analytically: 2-4x lim 40 5+3x x? - 2.x -15 lim x 5 2. 3. Find dy/dx of:

A: A number M is said to be the limit of a function f(x) at x=a if for any arbitrarily chosen positive…

Q: Find the limit using L'Hospital's Rule. e 2x – 1 lim x→0 sin x

A: We use L hospital's Rule

Q: (4x – 5y) lim (x,y)→(1,1) 5x² – 7y O -1/2 O 1/2 Limit DNE

A:

Q: For f(x) = x2, find dy using the definition, dx dy = lim dx Ду f(x+ Ax) - f(x) lim Ax→0 Ax Ax→0 Ax…

A:

Q: Example Find dy/dx for the function y = x² In (4x)

A:

Q: 70. J, f(x) dx may not equal lim , f(x) dx Show that 2x dx o x² + 1 diverges and hence that 2x dx x²…

A:

Q: S (2t)*dt lim x→ =? х* — 1

A:

Q: f(x) lim sin(5x) X I 0 -0.25 3 2 Estimate the limit numerically or state that the limit does not…

A: We have to find out limit

Q: Evaluate the limit *dx – x – 4aª lim 3 A) В) 1 C) D) 4 E)

A:

Q: 'e in + = "T 2n Find lim a

A:

Q: By using The definilion of the D Lim x (X+1)= o 2) Lin x Cos

A: Given: 1)limx→0x(x2+1)=02)limx→0x cos1x=0

Q: Ex let yct) soluton to the I.V.P y"-y'-2oy=0, yco) =3 , yto) = b If . Lim yL)= O find b?

A: Explanation of the answer is as follows

Q: D Find lim X,Y)→ (5,1) XY X+y or show it DNE.

A: We have to find limit

Q: 4. Evaluate the limit: lim sin arctan x V2 b. 2 1 d. DNE a. C.

A: Evaluate the given limit.

Q: Find the limit. lim ey sin P -(5, 0, -5) O 1

A:

Q: S, f(x) dr may not equal lim , f(x) dx. Show that 2x dx x* + 1 diverges and hence that 2x dx ? + 1…

A:

Q: compute dy/dx using the limit definition. y = 4 − x2

A:

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)