PART C 15. Use the definition of the derivative to evaluate each limit. e2+h – e? 1 a. lim h h→0 b. lim h→0 h

Q: Evaluate the given Integral 1. ſ csc x (cos2 x - 1)dx

A: Solution is done in step 2

Q: f'(x)= -+e²* +x°and f (1) = Find f(x) Given 5.

A:

Q: Obtain the differential equations satisfied by the given particular solution 2. y = 7- 2x +e* 3 1-…

A: Hi there! Thank you for your question. Unfortunately as per our guidelines we are restricted to…

Q: 6. lim f(x) = +o, lim f(x) = 0 x-1+ x-1- and f(-1) = -1

A: discontinuity

Q: 1 1. lim x-0+x e*

A: Given: limx→0+1x-1ex-1   So, simply we can write as; limx→0+1x-1ex-1=limx→0+ex-1-xxex-1

Q: 15 lbs 200 27° 12 lbs What is the approximate magnitude of the resultant.force? A 22.2 pounds. 24.8…

A: using component

Q: 1. Consider A = (0,4, 2), B = (6,0,0) and C = (3,0,-1). %3D %3D (a) Find the unit vector in the same…

A: B-2A+C=<6,0,0>-2<0,4,2>+<3,0,-1>…

Q: Obtain the differential equations satisfied by the given particular solution 2. y = 7- 2x +e*

A: The objective of the question is determine the differential equation.   Note -  As per our…

Q: 6. The radius of a sphere is measured to be 7 cm, with a possible error of + (1/10) cm. Estimate the…

A: Volume of sphere   V=3π​r3/4 Percentage error in volume    ΔV​×100/V=3×Δr​×100/r =3*1*100/10*7= 4.3…

Q: 2y(x? — у + х)dx — (x2 — 2у) dy %3D 0

A: I think mistake in question inplace of -ve sign.

Q: Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05 cm thick to a…

A:

Q: Please

A:

Q: Find the velocity and acceleration vectors in terms of u, and ug. de r= a cos 20 and 5t, where a is…

A:

Q: 2 sinh x Calculate the integral, J dx. 5+ 6 cosh x

A: Given :∫2sinhx5+6coshxdx

Q: 6. Vector, scalar or meaningless? Explain. ») (ä - 5) + (7 - E) b) (å x 5) – (¿ x đ) c) dlã x )

A:

Q: mine the value(s) of x where the slope of the tangent line is horizontal. Use exact valı…

A:

Q: 4. Evaluate the integral 2+ In? x -dx. x – x ln x (a) 3 ln |In a – 1| + 2(ln r – 1) + (In a – 1)2 +…

A:

Q: Determine the inverse Laplace transforms of: 2s²-5s-1 (a) (s+3)(s²+9)

A:

Q: -dx x2 +9 I x3 +ar-23 ton- (특) +C a. 3 b. 1 x³ t qx + 27 tam " ) + C b*3-9*+27€an )+c C. d.늘-9x- 2구…

A: Using substitution method, integration is done.

Q: Determine the antiderivatives of the following functions: 1. V1-4x² dx 12 2. 1+9x² dx 3. 4+(x-3)² dx

A:

Q: a²z B. For each of the following functions z, find azz and ду? a2z дx? дудх' дхду' 1. z %3D2x? — 5ху…

A:

Q: II. Let f(x, y, z) = z° sin a + Determine 2 dydzərəz'

A: We know, ∂2f∂y∂x=∂∂y∂f∂x

Q: Consider the piecewise function: 2x+8, x3 Determine the value of each limit. If the limit D.N.E.,…

A:

Q: 1. f(x) = V3x +2 2. f(x) = 2х-3. 4 %3D 5x+1

A: We know quotient rule of differentiation as follows  ddx{f(x)g(x)} = g(x) f'(x) - f(x) g'(x){ g(x)}2…

Q: f'(x)=-+e2* +x² and S(1) =. Find f(x) Given %3D

A:

Q: Find the 2nd derivative with complete solution y = 3x + 5 / x^2 + 4

A:

Q: For the function f(x), defined graphically, state the value(s) of x where the function is not…

A:

Q: Si cos3x cos4x dx 2 TT 6

A:

Q: If f'(2) = 5 then [4f(x) – x³]x=2 %3D dx Select one: O 32 O 8 O 28 O 20 O none

A: Given f'(2)=5To find ddx[4fx-x3]x=2

Q: Consider A = (0, 4, 2), B = (6,0, 0) and C = (3,0, –1). (a) Find the unit vector in the same…

A:

Q: I. Find the general solution of the following: dy 2x 1.- dx y dy 2. xy dx 3. dy = (6e3x+ 1)dx

A: We have to find the general solution.     According to our guidelines we can do only one question so…

Q: 2x^ + xt3 dx x+ x a. In lxl+Ź In Cx t1)+ tan-"c) tc b. In \xl-Į m (x2+1)+ tan-' Cx) tc in e, wone

A: The integration of the integral is  (2x2+x+3)/(x3+x).

Q: '9 — х? dx x2

A:

Q: Convert to a rectangular coordinate. Convert to a polar coordinates. 5T 10. 11. (-4,4)

A:

Q: #2

A: To find out the integration.

Q: For the following exercises, evaluate the integral. S(wew + w²ew*)dw 5.

A:

Q: Obtain the differential equations satisfied by the given puiiicular 3. y = e5x - 3x - x2 4. y = e3x…

A:

Q: 1. If f(x) = *, then f(x + h) = %3D 2. If f(x) =, then f(x + h) = 3. If f(x) then f(x + h) = Vx+2'…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Evaluate the guen -x>·dR,where conGists of the upper past F the cuafe x ty"=1 from "(-1,0) parabala.…

A:

Q: Find the nth term of the given infinite series for which n= 1, 2, 3, ... 1 1 +... 2x6 3x7 4x8 5x9 an…

A: Given 12×6-13×7+14×8-15×9+.....n is from 1,2,......... to infinity

Q: 27. Find the magnitude of the resulting force. Round to the nearest Newton. B: 11.1 N, 111° A: 10.0…

A: Solution: Given

Q: lim Vxe 2

A: Given query is to find limit of the expression.

Q: Matching Type. Match the functions in Column A with their corresponding antiderivatives in Column B.…

A:

Q: Analysis 3: Based on the design of the antennas, the Standard Absorption Rate (SAR) of RF power by…

A: Concept: The Trapezoidal Rule: Consider the continuous function f(x) on the interval [a, b]. Divide…

Q: To find two real numbers whose sum is 46 and whose product is maximum, we should find the maximum…

A:

Q: Solve the given initial-value problem y' + (tan.x)y = cos²x, y(0) = -1

A:

Q: tan () (9) sin (4) F. Evaluate the integral r2 cos ()

A: integration

Q: 4. Consider the curve with equation y = x* as shown in the diagram. A tangent line meets the curve…

A:

Q: 3. Which of the following is a true statementCirclc all that apply. (a) If lim an = 0, then the…

A:

Q: Express à to the vector (1, 4, 2). (3, 1, – 1) as B + C, where B is parallel to the vector (1,4, 2)…

A: