B. Directions: Using special functions, evaluate the following:

Q: 5x + 2 lim log + 6 10x + 12 ° X-

A:

Q: The diagonal of a cube can be derived by Pythagorean Theorem using the diagonal of a square and the ...

A:

Q: Below is a graph of the derivative of a function f. y 3| (x from -1.3 to 2) A.0 -0.5 -1 0.5 1.0 1.5 ...

A:

Q: What is the velocity vector? v(t) = ( Di+ ()i+ (1) k What is the acceleration vector? a(t) = () i+ (...

A:

Q: Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b). (Select all tha...

A: We know that Rolle's theorem , If y=f(x) is real valued function of real variable such that, (i) f(x...

Q: 1 Find the derivative of g(x) = Vx-1 Find f'(x) and f"(x) of f(x) = 11x³.

A: Here we have to find the derivatives of the given function.

Q: 2. In each figure, congruent parts are marked. a. List down the given congruent parts. b. Give addit...

A:

Q: Evalnate the fo llowing limits 1. lim 4x-5x+1 メ→ -4x? 2. lim I x²+5x -6 X- 4 lim (1x-7)* 3. 2.

A:

Q: [(x²-4)(12z–z')' dz

A: Given,            ∫z2-412z-z34dz

Q: Write z, and z, in polar form. Z1 = 7 + 7i, z2 = 4 21 = Z2 Find the product z122 and the quotients 2...

A: Since you have asked multiple part question, we will solve the first 3part of the question for you a...

Q: using implicit differentiation. dx Find sec (xy?) = (cosh x)(tanh z+v9) + 2 csc-1 (tan(y+ 1))

A: To find the derivative

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and...

A: Given   xy=4

Q: 5. Simpson's and Trapezium rules 1. A car's speed is recorded at 10 second intervals. The following ...

A: We need to use Simpson's rule to find distance.

Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given ...

A:

Q: Let y = 5x² + 5x + 3. Find the differential dy when x = 1 and dx = 0.1 %D %3D Find the differential ...

A: Topic = Derivative

Q: For the following exercises, find all points on the curve that have the given slope. 71 x= 4 cos t, ...

A: Given query is to find the points where slope is 0.5.

Q: Fg(x) = 1 Vx-1

A:

Q: 4. Which of the following statements about the definite integral is/are false? f(x)dx=1 II. f(ex)dx=...

A: Given three option We should check the condition is true or false And identify which is false

Q: A particular computing company finds that its weekly profit, in dollars, from the production and sal...

A: Since the student has posted many sub-parts of the question and does not mention any specific part, ...

Q: ity 5: Do what is asked. Show neat and complete solutions on your answer A Norman window is construc...

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question fo...

Q: Given g(x) ニ X-1

A: We know that, g'(x)=limh→0g(x+h)-g(x)hHere g(x)=1x-1Therefore g(x+h)=1x+h-1Thereforeg'(x)=limh→01x+h...

Q: du 13. (1 + t) - + u = 1 + t, t> 0 dt dr + r = te' dt 14. t In t

A:

Q: What

A: We will find sine and cosine values for given angle. 

Q: ....... Find the point of intersection of the line through (1, -3, 1) and (3, -12, 6), and the plane...

A:

Q: 2/3 Q31 3x-2x, [-1,1] =3(x)-2 2- -1/3 -1/3 2x 2(x"?-1)=0 -1/3

A:

Q: Use implicit differentiation to find y". y2 - x² = 6

A:

Q: Q3/B/ Find the value of unknown in the following 1 -2 7 9 5 6 ? 3 ? -2 7 1 6 1 -2 7 +4 ? 1 - 5 6 -3 ...

A:

Q: Let a = ci + jand b = 4i + 36j. Find c so that a and b are orthogonal. C = i

A:

Q: DO NOT include spaces in between 17 characters. * Compute m d (In (In y)) at y=e. dy Your answer

A: The objective is to compute the derivative at y=e.

Q: Find the following. a. da Pro b. da le 4] = %3D C. dr (5e 02] = %3D

A:

Q: DO NOT include spaces in between characters. * 1 Find f' (-) if f(x) 2 Your answer

A: Solution ) f(x)=1/x2 f(x)=x-2 Differentiate with respect to x  f'(x)=-2x-2-1 [d/dx(xn)=nxn-1 ] f'(x)...

Q: 1. Use the e - d definition of the limit to show the following: (a) lim(5x – 2) = 3 エ→1 (b) lim Vr =...

A: The objective is to use definition of limit to prove the above question.

Q: e area between the two loops of the limacon r = 1+2 sin 0.

A: We are asked to find the area between the loops.

Q: O g(x)= ( % x + %) X so at the point X, =O. x >0 9メ- x

A:

Q: Find the directional derivative of the function at the given point in the direction of the vector v....

A:

Q: Determine whether the improper integral diverges or converges. 1 e2x + e-2x dx O converges O diverge...

A:

Q: Find the equation of the tangent line to the curve y = x + 5x^2 - 3 which is passing thru point (1,3...

A:

Q: Write the expression as the sine, cosine, or tangent of an angle. 3 COS sin)sin() COS - 7

A: Note that: cos x cos y-sin x sin y=cos (x+y)

Q: 1. Define the function [In(x + 1)] cosh x + tan x ,x > 0 (sinh x) sec-(x - 2) f(x) = , X < 0 a. Show...

A: Here, the given function is: f(x)=[ln(x+1)] cosh x+tan x, x≥0(sinh x)sec-1(x-2).       x&lt;0

Q: 4x (log3 x)° (csc5 x) Vsinh(2x – 8) b. y= -

A:

Q: Find the area of the triangle with vertices P(1,3,–4), Q(0, 0,0) and

A:

Q: x2 3 |5 – x + C а. 5 – x3 - cos t dt 1 + sin t In 1+ sin(t)|+C b.

A: integration

Q: 6. Find the minimum surface area of a box that holds 2 cubic meters.

A:

Q: dt 20.5 t2+2t A - In|t? + 2t| + C B. 2ln +C C. In +C D. In + C

A: First we common out t2 from denominator and then put 1+2/t=u and differentiate both sides with respe...

Q: Ssin (y)cos(y)/3+ sin° (y) + 5e" dy

A:

Q: DO NOT include spaces in between characters. Compute g'(2) if g(x)=10**-2*. 16 Your answer

A: The objective is to compute g'(2).

Q: tude of 76. t shershec imber.

A: answer of given question is in step 2

Q: et –1 t2 – 3t + 5 lim t-0 t t2 – 1

A:

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

A: a)a→=-3 i + 8 jUnit vector as the same direction;u= a→a→ =(-3 i + 8 j)(-3)2+(8)2u=(-3 i + 8 j)73u=-3...

Q: 9. |(x – 1)² -

A: